P11 Lab Manual-Morris - Los Angeles Harbor College Lab Book Pt1.docx · Web viewTHE PHYSICS 11 LAB BOOK Book 1: Labs 1 – 19. TABLE OF CONTENTS MECHANICS AND PROPERTIES OF MATTER

THE PHYSICS 11

LAB BOOKBook 1: Labs 1 – 19

.

TABLE OF CONTENTS

MECHANICS AND PROPERTIES OF MATTER

1. Measurement .............................................................................................................. 12. Vector Addition ........................................................................................................... 73. Topographic Mapping ................................................................................................. 94. Scientific Method Pendulum .......................................................................................115. Acceleration Due to.....................................................................................................136. Simple Machines – Pulleys .........................................................................................157. Simple Machines – Lever, Wheel and Axle, Inclined Plane ........................................198. Newton's Second Law of Motion ................................................................................219. The Coefficient of Friction ...........................................................................................2310. Centripetal Force.........................................................................................................2511. Hooke's Law................................................................................................................2712. The Ballistic Pendulum ...............................................................................................2913. Moments and Center of Mass .....................................................................................3314. Archimedes' Principle .................................................................................................3715. Boyle's Law.................................................................................................................39

HEAT

16. Heat of Fusion of Ice ..................................................................................................4117. Heat of Vaporization of Water .....................................................................................4318. Specific Heat of Metals ...............................................................................................4519. The Coefficient of Linear Expansion ...........................................................................49

The Statistics of MeasurementThe Least-Squares Fit to Data

Experiment 1

MEASUREMENT

INTRODUCTION

This experiment will involve making various measurements of mass, length, and time using simple laboratory measuring equipment. The system of units we will be using is called the metric system or the Systeme International, hereafter referred to as "SI".

The SI unit of length is the meter. We will be using the meter stick, the vernier caliper, the micrometer, the tape measure and the wire gauge to measure this quantity.

The Meter Stick: The physical size of an object is a fundamental property, and the height, width and depth of an object is measured by its length along each dimension. Examine the meter stick in front of you. The meter stick is slightly longer than a yardstick, and is divided into 100 centimeters. Each centimeter is further divided into 10 millimeters, so there are 1000 millimeters in a meter. The millimeter can be abbreviated as mm, and the centimeter can be abbreviated as cm. Every measurement of length must be followed by its unit.

Whenever a meter stick or metric ruler is used, the result should be expressed to the nearest millimeter. For example, the length of one-third of a meter stick can be expressed as 333 millimeters, 33.3 centimeters or 0.333 meters. The left-hand edge of a meter stick is supposed to be at 0.000 meters, but its edge may be damaged or worn. The correct way to get an accurate measurement is to place the object being measured near the center of the ruler, read the position of the left edge of the object, read the position of the right edge of the object, and subtract one number from the other. For example, if the left edge is at 321 mm and the right edge is at 674 mm, the length of the object is 674 - 321 = 353 mm.

The Vernier Caliper – This device can measure to an accuracy of one-tenth of a millimeter, and all measurements obtained with this device should be quoted to this degree of accuracy. To use this device, the length to be measured is placed in the jaws of the caliper, and the jaws are then closed by pushing on the wheel to the right of the movable window. The measurement is found by reading the ruler visible inside the window of the movable jaw.

This reading is a two-step process:

First, look just below the window of the movable jaw. You should see eleven vernier lines, and for this step you use only the leftmost of these eleven vernier lines. That leftmost line points in between two ruler lines directly above it, seen inside the window. Write down the value of the ruler line on the left. The measurement will begin with this value.

Second, which of the eleven vernier lines has a ruler line directly above it? These vernier lines are numbered 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This number is placed after the value found in the first step. The vernier number 10 is never used.

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For example, suppose the vernier caliper has been set as shown:

Performing the first step, the leftmost vernier line (thick arrow) points between the ruler lines 11 mm and 12 mm. The ruler line on the left is 11 mm, so you would write down the value ’11. mm’. Performing the second step, the vernier line 3 (thin arrow) has a line directly above it, and so a 3 is placed after the previous value. The answer is 11.3 mm.

As a second example, suppose the vernier caliper has been set as shown:

Performing the first step, the leftmost vernier line points between the ruler lines 25 mm and 26 mm. The ruler line on the left is 25 mm, so you would write down ’25. mm’. Performing the second step, the vernier line 8 has a line directly above it, and so an 8 is placed after the previous value. The answer is 25.8 mm.

The Micrometer - This device can measure to an accuracy of one-hundredth of a millimeter, and all measurements obtained with this device should be quoted to this degree of accuracy. To use this device, the length to be measured is placed in the jaws of the micrometer, and the barrel is rotated until the jaws have closed. Warning! A large amount of force should not be applied when rotating the barrel, as this will strip the screw inside the barrel and ruin the micrometer. Close the jaws so that they are ‘finger-tight’. That means that when your fingers rotate the barrel with only light pressure applied, your fingers slide along the barrel and it does not rotate any more. Some of the micrometers have a small friction barrel on the right-hand side of the barrel, which will prevent the barrel from rotating

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30 40

window

vernier

20ruler

10

when too much force is used. If your micrometer has a friction barrel, use it to close the jaws.

This reading is a two-step process:First, look at the ruler between the jaws and the barrel. The left edge of the barrel

cuts across the ruler, which is measured in millimeters, and shows millimeter lines (on top) and half-millimeter lines (on bottom). Write down the value of the ruler line that is visible to the left of the edge of the barrel.

Second, which of the barrel lines is closest to the horizontal line on the ruler? The two-digit number of that barrel line (from .00 mm to .49 mm) is added to the value found in the first step. If this is confusing, open the jaws slightly until the barrel value is .00 mm, and the measurement is obvious. Then, slowly close the jaws until the barrel has returned to its former position. The correct value will be slightly smaller than the value obtained when the jaws were slightly open.

For example, suppose the micrometer has been set as shown:

Performing the first step, the ruler line 7.00 is the line that is visible to the left of the barrel, so you would write down the value ‘7.00 mm’. Performing the second step, 26 is the barrel line closest to the horizontal line, and so 0.26 mm is added to the previous value. 7.00 + 0.26 = 7.26, so the answer is 7.26 mm.

As a second example, suppose the micrometer has been set as shown:

Performing the first step, the ruler line 6.50 is the line that is visible to the left of the barrel, so you would write down the value ‘6.50 mm’. Performing the second step, 40 is the barrel line closest to the horizontal line, and so 0.40 mm is added to the previous value.

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horizontal linebarrel

0 5 30

25

0 5

40

ruler

6.50 + 0.40 = 6.90, so the answer is 6.90 mm. Notice that the answer contains a ‘0’ in the last place, to signify that the length has been measured to this level of accuracy.

EQUIPMENT & MATERIALS

Wire and nail samples Meter stick Wooden block BalanceVernier caliper Rock specimen Wooden sphere MetronomeMicrometer Tape measure Glass marble Wire gaugeStop clock

EXPERIMENTAL PROCEDURE

A. LENGTH

1. METER STICK: Measure the dimensions of the top of your student table to an accuracy of the nearest millimeter. Enter all measurements in the laboratory report at the end of this experiment.Area = length X width.

2. VERNIER CALIPER: Measure the sides of a wooden block, to an accuracy of a tenth of a millimeter. Measure the diameter of a wooden sphere.

3. MICROMETER: Measure the diameter of a glass marble, to an accuracy of a hundredth of a millimeter.

4. TAPE MEASURE: Measure the length and width of the classroom floor in feet and inches, using the 50 ft. tape measure. Convert to decimal feet (3 ft. 4 in. 3.33 ft., for example). Then convert your measurements into the SI system of units; 1 foot = 0.3048 meters. Calculate the area of the floor (length times width) in ft2

and m2. Notice that in the Imperial (English) system you have to convert to decimal feet before multiplying. In the metric system, calculations are easier.

5. WIRE GAUGE: Find the diameter of a small wire or nail by sliding it along the rim of the gauge (measured in inches). Multiply this by 25.4 to convert to millimeters, and check the result using the micrometer.

B. MASS

1. BALANCE: The SI unit of mass is the kilogram. In our lab, the balance is used to measure this quantity. Slide the two scale weights to their zero positions on the left-hand side, then calibrate by rotating the weight on the screw until the needle at the top of the scale is zeroed. The balance works by placing the mass to be measured on the left-hand pan, then sliding the two scale weights to the right until the needle is zeroed again. The mass of the object is the sum of the two scale weights, to an accuracy of one-tenth of a gram.

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Determine the mass of three items on the balance such as a block, a sphere and a rock.

C. TIME

1. METRONOME: The SI unit of time is the second. The stop clock we use owes its accuracy to the precise 60 Hz line voltage oscillations that the power company provides. Set the metronome at a reading of 120 by placing the top of the sliding weight just below ‘120’ on the metronome face. Use the stop clock to measure the amount of time the metronome takes to count out 100 beats, to a tenth of a second accuracy. Divide by 100 to get a measured time for 1 beat, to a thousandth of a second accuracy. The nominal time for 1 beat is determined from the ‘named’ value given as 120 beats per minute. This is the given value used in determining the percent difference. The percent difference is given by:

% difference =

measured value − given valuegiven value X 100%

The given value in a calculation of percent difference may be a value that has been determined by very precise experiments, or it may be a value expected from theoretical considerations.

2. PULSE: Time 20 beats of your pulse, to a tenth of a second accuracy. Repeat this four times to give a total of 5 measurements. Calculate the average value of your pulse rate by adding up your five measurements, then dividing that number by 5.

The deviation of each measurement is the measurement minus the average. Some of those deviations will be positive numbers and some will be negative. When you square each deviation, the result must be either zero or a positive number.

Calculate the standard deviation. This is the typical scatter of a single measurement around the average.

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Experiment 2

VECTOR ADDITION

INTRODUCTION

A vector is defined as a mathematical representation of a quantity that possesses both magnitude and direction. A scalar quantity has only magnitude. In this experiment we will add a number of forces using a force table and then compare the sum with that obtained by vector addition.


3 clamp-on pulleys 1 sheet of blank paper Slotted masses RulerCircular (bubble) level 3 Mass hangers, 50 g Force table Protractor


1. Place the circular level on top of the force table, and adjust the feet until the force table top is horizontal. Arrange three pulleys with strings on the force table as shown in Figure 1. Two of these will be forces A and B and the third, or equilibrant, will be force C. The magnitude of the equilibrant will be chosen to balance the forces A and B, creating a total force of zero.

Fig. 1. Force Table, Top View

2. Use masses (slotted masses plus the mass of each hanger) of 200 grams each to create the forces A and B. Place A and B with a small angle of about 40o between them (that is, at +20o and –20o), and balance them with a suitable amount of mass at C. Record the magnitudes and angles for A, B, and C in the laboratory report. The system is balanced when the central pin may be pulled up and the ring released without changing its centered position.

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3. Repeat step 2, this time with a larger angle of 60o between them.

4. Repeat step 2 again, using an angle of 90o between them.

5. Repeat step 2 again, using an angle of 140o between them.

6. Draw a labeled free-body diagram to scale on the sheets at the end of this lab for each of the cases in steps 2 - 5. Let 200 grams on the force table be represented by 5.0 cm, so the magnitude of each force can be converted to a length; multiply the number of grams by 0.025 to get the length in centimeters. Using the parallelogram method, add the vectors A and B on the same sheet to find their resultant vector. Draw the equilibrant (Force C) along the negative x-axis. Compare the resultant so obtained with the magnitude and direction of the equilibrant. Are the equilibrant and the resultant exactly opposite and equal to each other?

Shown in Figure 2 is an example of how parallelogram addition works:

We wish to add vectors A and B. We move them so that their tails touch. (Note that one can move a vector so long as the direction is not changed.) Make a parallelogram out of A and B so joined. The diagonal of the parallelogram is called the resultant.

Fig. 2 Parallelogram Method of Vector Addition

7. Place 3 unequal forces at unequal angles in equilibrium on the force table. Draw to scale a force polygon on a blank sheet of paper, by placing the tail of arrow B on the head of arrow A and the tail of arrow C on the head of arrow B, as shown in Figure 3. Show the amount by which the polygon does not close by a labeled arrow. Measure its value and indicate this as the resultant error.

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Fig. 3 Typical Force Polygon

Experiment 3

TOPOGRAPHIC MAPPING

INTRODUCTION

In this experiment the instructor will give you an overview of how to read topographic maps, which are maps that describe the physical features of part of the Earth’s surface.


Topographic map 360o protractor RulerString & scissors Paper

LABORATORY REPORT

Place the answers to the following questions on the blank paper, with your full name printed neatly in the upper-right corner.

1. Name the highest mountain and give its elevation.

2. Which town has the highest elevation?

3. Which mountain has the steepest slope?

4. What is the latitude and longitude (to the nearest tenth of a minute of arc):

(a) of the center of Norton?

(b) of the summit of Bald Peak?

(c) of the summit of White Mountain?

(d) of the mine? (Draw the mine’s line of latitude and line of longitude on the map.)

5. How far is Blue Lake from Norton?

6. Is Dixon or Rockville closer to Norton?

7. How long is the railroad tunnel (use the edge of a sheet of paper to transfer the scale)?

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8. How far is Rockville from Norton by highway? Place a length of string along the highway, then straighten it and compare it to the scale.

9. How much farther is this than the straight-line distance (the U.S. average is l5 percent longer)?

10. How long would it take to walk from Rockville to Norton?

11. What direction would you travel from Dixon to Rockville? Directions are measured from true north (0o) through east (90o).

12. Is the trip from Dixon to Rockville uphill or downhill?

13. What is the true direction from White Mt. to Bald Peak?

14. What is the magnetic direction from Summit Mt. to Bald Peak?

15. Starting at the peak of White Mt., you fly horizontally 125o true for 3 minutes at 120 mph, turn and fly 270o true for 4 minutes and then turn to 180o true for 1 minute while rising 500 ft. Draw these horizontal motions on your map. What is your final latitude, longitude and height above sea level?

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Experiment 4

SCIENTIFIC METHODPendulum

INTRODUCTION

This experiment will use the scientific method to determine what factors enter into the value of the period of a pendulum. The period of a pendulum is the time for one complete swing to and fro, and is given theoretically by the following relation:

T=2π √ Lg

where T is the period, L is the length, g is the acceleration due to gravity = 9.80 m/s 2 and = 3.14159…

The factors to be investigated as possibly affecting or not affecting the period will include: length of string, mass of the bob, size of the bob, composition of the bob, and amplitude of the swing.

As much as possible in this experiment, each factor will be varied by itself; that is, the other factors will be kept constant while the effect of the one under consideration is studied. Keep the amplitudes of the swings just large enough so that the pendulum will complete the 25 swings. Avoid amplitudes larger than 10o from the vertical.


Support rod Table clamp Metal cubes Pendulum clampString, scissors Stop clock Protractor Meter stickBalance Metal spheres Wooden spheres


A. Effect of Length

1. Attach a string to a heavy metal sphere and suspend it from the pendulum support. Start with a long length (75.0 cm measured from the edge of the support to the center of the ball) and measure the time taken for 25 complete swings. Use a stop clock to measure the time. The period will be the total time divided by 25.

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2. Repeat step 1 three times, each time shortening the string from the previous time (lengths of 50.0, 40.0 and 30.0 cm will be convenient). Does the length of the string have any effect on the period?

B. Effect of Mass of Bob

1. Replace the bob with a wooden sphere of about the same size as the metal sphere, but of less mass. Again count the time for 25 swings. In all cases, be sure that L = 75.0 cm, measured from the edge of the support to the center of the sphere, accurate to the nearest millimeter! Now that you have changed the mass of the pendulum bob significantly, is the period the same or different from that for the steel sphere?

C. Effect of Shape

1. Use the same length as in Part B, and replace the bob with a large metal cube. Time 25 swings. Does the shape make any difference?

D. Effect of Size

1. Use the same length as in Part B, and replace the bob with a small metal sphere of about the same mass as the wooden sphere in Part B. Time 25 swings as before. Any difference?

E. Effect of Amplitude

1. It is no longer necessary to keep the amplitude of the swings small. Use the original metal sphere and the same length as in Part B, and time 25 swings with amplitudes of 30o and 45o from the vertical. Can you observe any change?

F. Theoretical and Experimental Determination of the Period

1. The time for a pendulum to swing from the left extreme to the right and back to the left again is called the period, T. Determine experimentally the length of a pendulum which will have a period of exactly 2.0 seconds for small amplitude oscillations, to the nearest millimeter.

2. Calculate the theoretical length of a pendulum having a period of 2.0 seconds from the formula, by squaring both sides to get T2 = 42L/g, and solving for L to get L = T2g/42. Compare this with the value you obtained in the previous step by computing the percent difference.

% difference =

measured value − given valuegiven value X 100%

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Experiment 5

ACCELERATION DUE TO GRAVITY

INTRODUCTION

When objects relatively close to the Earth's surface are allowed to fall freely, they undergo uniformly-accelerated motion. In today's experiment, we will measure the acceleration due to gravity which has the value of:

9.80

The unit of meters per second squared means that the velocity is increasing by 9.80 m/s each second.

A free fall apparatus will be used to make a paper strip record of the distance the object falls as a function of time. This apparatus consists of a plastic and metal object that falls freely between two vertical conducting wires with a tape strip of wax paper between the object and one of the wires. The spark timer which is used with this apparatus is a fast timing device which supplies a high voltage pulse at constant time intervals (for example, 1/60 s). The free fall apparatus has an electromagnet which holds the object until the timer is activated.

The voltage supplied by the timer is great enough to jump between the conducting wires only when the metal object is between them. When this occurs during fall, a series of holes is burned in the wax paper. The holes on the tape are equal time intervals apart and give the vertical distance of fall as a function of time.

In our analysis of the paper tape we will make use of the following kinematic equation:

vaverage = v = change in dis tan cechange in time

= ΔdΔt

or, in other words, the distance traveled in an interval divided by the time gives the average velocity for that interval. However, since we are interested in instantaneous velocities at certain instants of time, we can make use of the fact that the instantaneous velocity is equal to the average velocity at the midpoint in time of the interval. So when successive instantaneous velocities are plotted as a function of time, we should obtain a straight-line graph, the slope of which is equal to the acceleration of gravity.

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.second2meters


Free fall apparatus Ruler Masking tape Clear plastic triangleSpark timer, 1/60 sec. Meter stick Free fall tape 1 sheet of graph paper


1. The paper record tape will already be made for you, or your instructor will assist you in making one. Use a piece of masking tape to secure your paper strip to the table. Starting with the first well-defined hole, draw a straight line through it perpendicular to the length of the tape. Do this for every other hole and number them 0, 1, 2, 3, 4, 5 etc., as shown in the diagram below.

2. Place the edge of the meter stick a few millimeters to the left of the zero hole, then measure and record the position of each numbered hole. Putting the meter stick on edge with the gradations in contact with the paper will help to avoid parallax errors. Tape the meter stick to the table. Make your readings to the nearest millimeter and record them in the data table.

3. Subtract each reading from the one immediately following it. This difference gives the distance traveled during successive 1/30-second time intervals. Divide these distances by the time interval (1/30 s) to obtain the average velocity for the interval and record this in the data table. These averages are the instantaneous velocities at the midpoint in time of the interval which is at the hole between the numbered holes.

4. Plot a graph with time on the horizontal axis and average velocity on the vertical axis. Remember that each value of average velocity should be plotted so as to correspond to the value of time at the middle of the interval for which the velocity was calculated. Draw a single best straight line through the points (this means the same number of points on both sides of the line and the total distance of the points to the line being the same on both sides of the line). The slope of the graph obtained should be equal to the acceleration of gravity. The y-intercept will give the velocity at the zero hole. Record your value of acceleration in the laboratory report and calculate the percent difference.

5. Remove masking tape from the table and the meter stick before leaving.

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Experiment 6

SIMPLE MACHINESPulleys

INTRODUCTION

In this lab we will study a simple machine called the pulley. By making actual measurements of input force, output force and appropriate distances, the ideal mechanical advantage (IMA), the actual mechanical advantage (AMA), and the efficiency can be determined for each case tested. All the simple machines that we will study are governed by the physical law called the conservation of energy, that is, the energy put into the system equals the energy you get out. For our system this can be expressed by the following equation:

INPUT FORCE X DISPLACEMENT of INPUT = OUTPUT FORCE X DISPLACEMENT of OUTPUT + FRICTIONAL LOSS & ROTATIONAL LOSS

Some other definitions that you will need are:

IMA =

DISPLACEMENT OF INPUT FORCEDISPLACEMENT OF OUTPUT FORCE

AMA =

OUTPUT FORCEINPUT FORCE

EFFICIENCY =

AMAIMA X 100%


2 Single pulleys Pendulum clamp Support rod2 Double tandem pulleys String, scissors Hooked mass set2 Triple tandem pulleys Meter stick Ruler

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250 & 500-g spring balance Table clamp Electronic balance


1. Calibrate your spring balance by holding it vertically without any mass attached, and sliding the scale face until it reads zero. All measurements must be taken with the spring balance held in this position, not sideways or upside-down.

2. Arrange the pulleys as indicated in the diagrams. Do one set-up at a time.

3. The ‘Output Force’ is the force that the pulley system lifts up, and is equal to the ‘Mass of Brass Cylinder’ added to the ‘Mass of Movable Pulley’, if a pulley is being moved up and down. Enter the masses in the table.

4. The ‘Input Force’ is the force that is exerted by you onto the pulley system, and is equal to the ‘Spring Balance Reading’ added to the ‘Mass of Spring Balance’, if the spring balance is adding its weight to the force you are exerting. Determine the ‘Spring Balance Reading’ while the brass cylinder is moving slowly upwards at constant speed. Be sure to make your loads progressively larger as you go from type I to type IV, in order to obtain a large (and accurate) reading from the spring balance.

5. The ‘Displacement of Input Force’ is the distance the scale travels, measured against a meter stick, and the ‘Displacement of Output Force’ is the distance the brass cylinder travels upward. Measure both at the same time, to the nearest millimeter. It is convenient if the ‘Displacement of Input Force’ is somewhere between 0.400 and 0.600 meters.

6. Compute the ideal and actual mechanical advantages, and the efficiency for each of the eight cases.

Pulley Diagrams

I a. Single, Fixed I b. Single, Movable

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II a. Singles, Movable II b. Singles, Movable

III a. Double Tandem, Movable III b. Double Tandem, Movable

IV a. Triple Tandem, Movable IV b. Triple Tandem, Movable

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Experiment 7

SIMPLE MACHINESLever, Wheel and Axle, Inclined Plane

INTRODUCTION

In this experiment we will study three types of simple machines; the lever, the inclined plane, and the wheel and axle. By making actual measurements of output force, input force and appropriate distances, the ideal mechanical advantage IMA, the actual mechanical advantage AMA, and the efficiency of each case will be determined. Refer to Experiment 6 for the definitions of these terms. Measure all distances to the nearest millimeter.


Table clamp String & scissors Knife-edge stand Hall's carriageMeter stick Knife-edge clamps Double pan balance Clamp for wheelSupport rod 250-g spring balance Mass hanger, 50 g Transfer caliper Inclined plane Hooked mass set Slotted mass set Wheel and axle


A. LEVER

Use a meter stick, knife-edge clamp and support stand to create a lever and fulcrum. Use hooked masses for the output force (the load, designated by L) and a small spring balance for the input force. For all three arrangements, place the fulcrum near the 50.0-cm mark so the meter stick alone balances. With the fulcrum at this point, the weight of the meter stick

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does not contribute to the readings. Be sure to zero the spring balance first.

1. Arrange the equipment as a first class lever. The load can be suspended from a small loop of string. Record the load, input force, and distances of each from the fulcrum. For the first class lever only, the mass of the spring balance must be added to the spring balance reading to give the total input force. Choose an input force lever arm (the distance from input force to fulcrum) that is different from the load lever arm (distance from load to fulcrum).

2. Arrange as a second class lever. Determine the input force for a load of 500 grams using a spring balance.

3. Arrange as a third class lever. Determine the input force for a load of 100 grams using a spring balance.

4. For all cases, calculate the actual and ideal mechanical advantage and the efficiency. The AMA is the load divided by the input force. The IMA is the input force lever arm divided by the load lever arm.

B. WHEEL AND AXLE

1. Set up the wheel and axle supported by the table clamp and support rod. Thread a length of string through the back of the wheel and axle apparatus, into the hole closest to the center. Tie a knot at the back end so the string cannot fall through the front, and tie a loop at the front end to support the mass holder. Repeat for the hole on the outermost rim, with a loop for another mass holder at the end. Arrange first as in case A, shown below, with the load attached to the innermost string, wound around its circle.

2. The wheel radius is the distance from the center of rotation to the point where the input force is applied. The axle radius is the distance from the center of rotation to the point where the load is applied. Measure these by using the transfer caliper to find the diameters accurately, then divide by 2. Use 550 grams for the load. Use other slotted masses for the force and add them to the holder until the force is just enough to cause the load to rise with a steady velocity, once the system is given a slight push.

3. Case B: Move the load to the middle position and repeat step 2.

4. Case C: Move the load to the outermost position and repeat step 2.

5. Calculate the AMA (load/input force), IMA (wheel radius/axle radius), and efficiency for each case.

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C. INCLINED PLANE

1. Use the Hall's carriage with the inclined plane set at 30o. Determine the mass of the carriage. The input force F is provided by the mass hanger and the slotted masses. The displacement of the input force equals the distance the cart moves along the hypotenuse.

2. Place the cart at the bottom of the plane. Add just enough mass to the hanger so that the hanger descends at constant velocity. The vertical distance is the distance any point on the cart has moved vertically from the beginning to the end of the trip. Calculate the AMA, IMA and efficiency.

3. Make another trial as in step 2, using 400 grams in the cart.

Experiment 8

NEWTON'S SECOND LAW OF MOTION

INTRODUCTION

This experiment will verify that acceleration is directly proportional to force if mass is kept constant, and is inversely proportional to mass if force is kept constant. In other words, F = ma where F is the net force, m is the mass being accelerated and a is the acceleration. The pulley system shown to the right, with unequal masses on each side will be used. Historically, this arrangement has been called the Atwood's machine.


2 sets of slotted masses Wheel & axle Thick string Stop clock2 one-kg mass hangers Two-meter stick Scissors Table clampWheel & axle clamp Support rod Ruler Foam pad

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A. PRELIMINARY

Set up the wheel and axle at the top of the support rod clamped to your table, and loop a piece of string approximately 1.9 meters long over the largest wheel, with a mass hanger at each end. Choose one side to be the descending side, and place a foam pad beneath it for the mass hanger to land on. To determine the correction for friction, add small masses to the descending side until that side, once started with a small push, descends with constant velocity. Be sure to determine this as accurately as possible, to the nearest gram. This is the friction allowance mf ; leave this amount on the side of the pulley that is descending at all times, for both parts B and C. Write down the mass of the friction allowance mf, and the mass of the pulley mp (printed on the pulley), on the data page.

Warning! Never crouch beneath the pulley; you could be injured if the string snaps. If a mass falls onto the floor, kick it away from the pulley before picking it up.

B. DRIVING FORCE KEPT CONSTANT

1. Add 20 grams to the descending side, so m1 = 1.020 kg and m2 = 1.000 kg. Measure to the nearest millimeter the distance that the descending mass will fall (~1 meter), with the string over the largest wheel of the pulley.

2. Time the fall of the descending side, to the nearest tenth of a second. Calculate the average velocity, final velocity and experimental acceleration from:

vaverage = Dis tance of fall

Time of fall (Eq. 1)

vfinal = 2vaverage (Eq. 2)

aexperimental =

v final

Time of fall (Eq. 3)

3. Theoretically, F = ma, where F is the (small) amount of force creating the acceleration, and m is the (large) amount of mass being accelerated. The force is the weight of the excess mass (m1 – m2) on the descending side, and the magnitude of this force is F = (m1 – m2)g, where g = 9.80 m/s/s. Calculate the force F.

4. The mass being accelerated is m1, m2, mf and the pulley as it rotates. Most of the mass of the pulley is not along the rim, and does not experience the full amount of acceleration. The pulley needs only one-third the force to accelerate its rim in rotational motion, as it would need to accelerate by moving in a straight line. To take this into account, only one-third of the pulley’s mass mp needs to be used in the calculation of mass. Calculate m = m1 + m2 + mf + (1/3)mp to determine the effective mass being

- 22 -

accelerated.

5 F = ma can be rewritten as a = F/m. Calculate atheoretical from the values of F and m in the data table. Find the percent difference between the theoretical and experimental values of the acceleration.

6. Add 100 grams to each pulley, and repeat steps 2 – 5. Notice that the force (m1 – m2)g remains constant, but the total mass that is being accelerated increases.

7. Repeat step 6 twice, to test F = ma for different amounts of mass.

C. MASS KEPT CONSTANT

1. Remove the added 100-gram masses, so the descending side has 1000 grams plus m f plus the 20 grams that accelerate the system, and the ascending side has 1000 grams. Add four 5-gram masses to the ascending side, so the descending side descends with constant velocity.

2. Move two of the 5-gram masses from the ascending side to the descending side, so m1 = 1.030 kg and m2 = 1.010 kg. Repeat steps 2 – 5 of part A.

4. Move another 5-gram mass from the ascending side to the descending side, and repeat steps 2 – 5 of part A. Notice that the force that creates the acceleration is increasing, but the total mass that is being accelerated remains constant. Repeat this one more time, moving the last 5-gram mass from the ascending side to the descending side.

Experiment 9

THE COEFFICIENT OF FRICTION

INTRODUCTION

In this experiment, the force laws governing sliding friction between dry surfaces will be investigated. We will use wood-on-wood surfaces. The force of kinetic friction fk is parallel to the two surfaces in relative motion, and follows the relation

fk = kN

where N is the normal force (the force of contact perpendicular to the two surfaces) and k is the coefficient of kinetic friction.

- 23 -

The forces acting between surfaces at rest with respect to each other are called forces of static friction and follow the relation:

fs sN

where s is called the coefficient of static friction.The above two relations will be verified by measuring the frictional forces associated

with increasing values of normal force. A plot of frictional force vs. normal force should yield a straight line, the slope of which is equal to the coefficient of kinetic friction.


Ruler Friction board Friction blockRight-angle clamp Electronic balance String, scissorsSupport rod, short Small rod for friction board Table clampSpirit level Mass hanger, 50 g InclinometerClamp-on pulley Slotted masses Meter stickPlastic triangle 1 sheet of graph paper


1. Place the board flat on the table. If the carpenter’s level shows that the board is not horizontal, the board can be leveled by placing strips of paper towel beneath it. Attach the clamp-on pulley to the end of the board and let the pulley extend over the end of the table.

2. Use the electronic balance to determine the mass of the block, and attach the string to the block. Lay the string over the pulley and attach the mass holder to the lower end of the string.

3. Place just enough mass on the mass holder so that the block moves at a constant speed, after it is given a slight push to get it started. The mass needed to move the block is the mass on the mass holder plus the mass of the mass holder itself. You should be able to determine this to the nearest gram.

4. Place some mass (~100 grams) on top of the block to increase the normal force, and

repeat step 3. As before, the block must not gain speed, but nevertheless continue moving at a constant speed. The total weight on the board is the total mass on the board (the mass of the block plus the mass added to the block) times the local acceleration of gravity. That is, W = mg, with g = 9.80 m/s/s and m in kilograms (1 kilogram = 1000 grams).

- 24 -

5. Repeat step 4 three more times, each time with a different mass on top of the block in order to show the effect of changing the normal force.

6. Plot the force of friction (which equals the weight needed to move the block) on the vertical axis vs. the normal force (which equals the total weight on the board) on the horizontal axis. Label both axes, and give the graph a title that described what was occurring to generate the data.

7. From the graph, determine the coefficient of kinetic friction as the slope of the straight line that passes as close as possible to all the data points.

8. Remove the string and weights from the block and the pulley from the board. Place the board at an angle to the horizontal by inserting the small rod through the long hole drilled through the side of the board, and supporting this rod on the vertical support rod clamped to your table. To determine the critical angle of friction, slightly loosen the clamp holding the board to the vertical support and smoothly increase the tilt of the board until the block slides down the board of its own accord, without giving it a slight push to get it started. Tighten the clamp at this position and measure the angle from the horizontal with the inclinometer. Repeat this step two more times and determine the average angle. The tangent of the angle is the coefficient of static friction.

Experiment 10

CENTRIPETAL FORCE

INTRODUCTION

In this experiment we will study the motion of an object traveling on a circular path, in order to verify the equation for centripetal force. A small object of known mass, m, will be forced to move in uniform circular motion. The centripetal force will be determined directly and then calculated from measurements of the radius and the speed. The following relation will be verified:

Fc = mv2r (Eq. 1)

where m is the mass of the revolving object, v is the speed of the revolving object, and r is the radius of the orbit of the revolving object .

- 25 -


Thistle tube String & scissors Balance50-g & 100-g hooked masses Rubber stopper, No. 5 Meter stickStop clock Red marker pen


1. Measure the mass m of the stopper. Tie it securely to a string that is about 2 meters long, and thread the other end of the string through the top of the thistle tube. Tie this loose end to the 0.050-kg hooked mass, which will function as the hanging mass M. It is the weight Mg of this mass that creates the force of tension in the string, which then functions as the centripetal force.

2. While the string is held taut, adjust the position of the thistle tube so that the distance from the center of the revolving mass to the center of the wider opening of the thistle tube is r = 0.500 meters, as shown in the diagram on the previous page. Be sure to measure this to the nearest millimeter. Use a red marker pen to place a mark on the string at the base of the thistle tube.

3. One student can now swing the revolving mass in a horizontal circle above the student’s head. Maintain a steady swing, keeping the mark as close to the bottom edge of the thistle tube as possible. Hold onto the thistle tube, but not the string, while the mass is revolving.

4. Another student, using the stop clock, can measure the total time for 25 revolutions for a radial distance of r = 0.500 meters. The time for one revolution is the total time divided by 25.

5. The speed is given by the formula:

v = circumference

time for one revolution = 2πrt

where r is the radius of revolution and t is the time for one revolution.

- 26 -

6. Repeat the experiment for r = 0.750 m and r = 1.000 m.

7. Repeat the experiment with M = 0.100 kg and the same lengths as above.

Experiment 11

HOOKE’S LAW

INTRODUCTION

The purpose of this experiment is to show that, to a good approximation, a spring’s behavior can be described by Hooke's law:

Force = - kx.

In this equation, ‘Force’ is the restoring force that the spring exerts upwards, trying to restore the spring to its original position, and x is the displacement of the lower end of the spring downwards from its original position. The factor k is the spring stiffness constant, which is often called Hooke’s constant or the spring constant. Since the force that we will supply is in the same direction as the displacement, we can rewrite the equation as:

- 27 -

F = kx

where F = mg is the downward force applied to the spring, due to the weight of the mass m attached to the bottom of the spring. A graph of applied force vs. displacement which yields a straight line will verify that the spring obeys Hooke's law.

A spring oscillates with simple harmonic motion (motion that is sinusoidal with respect to time) if an attached mass is given a displacement and then released. The relationship between the period of oscillation and Hooke's constant is given by:

T2 = 42M/k, or T = 2√ Mk

where T is the period of oscillation (time for one complete cycle) and M is the oscillating mass. A graph of the square of the period vs. the oscillating mass M which yields a straight line, will verify that the spring oscillates with simple harmonic motion.

EQUIPMENT & MATERIAL

Large brass spring Clear plastic straightedge Support rodPendulum clamp Table clamp Meter stickElectronic balance Hooked mass set Stop clock2 sheets of graph paper


1. Attach a pendulum clamp to the support rod and hang the spring. Attach small increments of mass (50 grams or so) and measure the displacement of the bottom of the spring from its original position. Take the spring to no more than about three times its original length. If the spring is stretched longer than this, you might exceed the elastic limit of the spring and permanently alter its shape. The applied force is the weight of the attached mass, mg, where g = 9.80 m/s2.

2. Make a plot of applied force (on the vertical axis) vs. displacement (on the horizontal axis). Find the spring constant from the slope of the straight line on the graph that passes as closely as possible through the data points.

3. Re-attach one of the masses used before, then pull it down several centimeters and release. Keep the motion of the spring only in the vertical direction by pulling straight down. Measure the time for 25 complete oscillations. One oscillation occurs as the mass moves from its lowest point to its highest point and back to its lowest point again. Compute the observed period of oscillation, from the time for 25 cycles.

4. Repeat step 3 for three other masses.

- 28 -

5. The attached mass is not the only mass that is oscillating. The bottom of the spring is fully oscillating as well, with the rest of the spring oscillating to a lesser extent. To take this into account, the equation for the square of the period uses the oscillating mass, which equals the attached mass plus one-third the mass of the spring:

M = oscillating mass = attached mass + 1/3 (mass of spring)

Calculate the theoretical period, from your values of M and k.

6. Plot the square of the observed period vs. the oscillating mass. Explain any deviation from a straight line.

Experiment 12

THE BALLISTIC PENDULUM

INTRODUCTION

In this experiment, the speed of a projectile will be measured in two different ways; through the use of conservation laws, and through the equations of projectile motion.

The Laws of Conservation of Momentum and Conservation of Energy

A ball of mass m is fired at an unknown speed v, and collides with a pendulum of mass M. After the collision, the pendulum swings in an arc and comes to rest at a vertical

- 29 -

height h above the starting position.Momentum is mass times velocity. According to the law of conservation of

momentum, the total momentum of the ball and (motionless) pendulum before the collision must equal the momentum of the ball and pendulum immediately after the collision:

mv + M0 = mV + MV. (Eq. 1)

Solving for v gives

v = m + M

m V .(Eq. 2)

So, the initial velocity v of the ball can be determined if the velocity V of the ball and pendulum immediately after the collision can be determined.

The law of conservation of energy states that the kinetic energy of the ball and pendulum immediately after the collision must equal the gravitational potential energy of the ball and pendulum when they have risen to the top to the arc:

½(m + M)V2 = (m + M)gh. (Eq. 3)

This can be solved to get

V = √2gh , (Eq. 4)

and this value of V can be substituted into Eq. 2 to get the initial velocity v of the ball.

The Equations of Projectile Motion

A ball of mass m is fired horizontally at an unknown speed v, and lands on the floor a time t later, having fallen through a vertical distance y and a horizontal distance x. The equation of projectile motion y = ½gt2 can be solved for the time of flight:

t = √ 2 yg . (Eq. 5)

The equation of projectile motion x = vt can then be solved for the initial velocity of the ball:

v = xt . (Eq. 6)


Ballistic pendulum One-meter stick RulerPlumb bob Two-meter stick 2 pieces of cardboard

- 30 -

Masking tape Spirit level 4-inch “C” clampPlain and carbon paper Electronic balance


A. Initial Velocity from Conservation Equations:

1. Use the spirit level to level the apparatus. Determine the mass m of the ball; the mass M of the pendulum is indicated on the pendulum.

2. Place the ball on the end of the gun rod. Compress the spring by pushing on the ball until the gun is cocked. The pendulum should hang freely and motionless.

3. Pull the trigger, firing the ball into the pendulum and onto the rack. Warning! Do not fire the gun if anyone is in front of it. Repeat 6 times, each time recording the notch on the rack in which the pawl rests. The pawl is the little catch that stops the pendulum at its maximum height.

4. Take the average of these six positions and place the pawl at this position. The center of mass of the pendulum is indicated by the tip of the pointed projection on the side of the pendulum. Determine the height h of the center of mass above the initial freely-hanging position, to the nearest millimeter.

5. Calculate the velocities V and v.

6. As a check, calculate the initial momentum and final momentum; according to the law of conservation of momentum, they should be approximately equal. Calculate the initial kinetic energy and the final gravitational potential energy; they should be approximately equal as well. If m is in kilograms and v is in meters/second, the unit of momentum is kgm/s and the unit of energy is Joules.

B. Initial Velocity from Projectile Motion Equations:

1. Level the ballistic pendulum apparatus and clamp it lightly to the table.

2. Hold the pendulum out of the way by placing it on the top of the rack, so the ball misses it completely. Place a large piece of cardboard against the wall, so that after striking the floor the ball will hit the cardboard, not the wall.

3. Place another large piece of cardboard on the floor in the approximate location of impact (about two meters away) and tape it securely to the floor. You may need to rearrange the tables to create enough room. Do a single test firing to locate the area of impact and tape a piece of plain and carbon paper at this location in order to record the exact point of impact.

4. Perform six firings and take the average of the locations as the point of impact. Measure the vertical distance y and horizontal distance x the ball has traveled to this average location, to the nearest millimeter.

5. Calculate the time of flight t, and the initial velocity v.- 31 -

6. Determine the percent difference between the initial velocity obtained in these two different ways.

- 32 -

Experiment 13

MOMENTS AND CENTER OF MASS

INTRODUCTION

For a body to be in static equilibrium, the vector sum of the forces F acting on it must be zero and in addition, the algebraic sum of the clockwise and counterclockwise torques must be zero. These conditions can be stated mathematically as follows:

F = 0 = 0

The first condition is concerned with translational equilibrium and the second condition is concerned with rotational equilibrium. The first condition ensures that the body is not moving (static case) or else is moving with constant velocity. The second condition

- 33 -

ensures that there are no unbalanced torques acting on the body (static case), or else the body is rotating with constant angular velocity. The magnitude of the torque is equal to the product of the lever arm and the component of force perpendicular to the lever arm.

The principle of moments (torques) will be used in this experiment to find the center of mass of two non-homogeneous bars. One is a meter stick modified by weighting one end, and the other is a bar which can be placed at a random angle.

Also, we will use the principle of moments to find analytically the forces of compression and tension in a model crane boom. This result will be compared with experimental measurements.


Knife-edge clamp Knife-edge support stand String3 right-angle rod clamps Spring balance, 500 grams ScissorsWeighted meter stick Non-concurrent forces apparatus 2 table clampsHooked mass set Long support rod 3 rod pulleysDouble pan balance Short support rod Protractor Heavy meter stick with hole at end


A. Center of Mass of a Weighted Meter Stick

1. Determine the mass of the special meter stick which has a metal bar of unknown mass attached to one end. Consider this weighted meter stick as a single object for the purpose of finding its center of mass.

2. Attach a knife-edge clamp to the midpoint of the special meter stick, set it on the knife-edge support stand, and hang three different standard masses from small loops of string positioned at random locations along the stick as shown in Figure 1. Adjust the positions of the masses until the system is balanced. Measure all distances from the fulcrum, with d as a negative number if the position is to the left of the fulcrum, and as a positive number if the position is to the right of the fulcrum.

Fig. 1

3. Solve the torque equation for dstick, the distance of the stick’s center of mass from the fulcrum. Show your calculations. Use this number to find the position of the center of mass as a reading on the ruler.

- 34 -

4. Repeat for three other masses at different positions. The two values so obtained for the center of mass should be within a few millimeters of each other. As a further check, remove all extra masses and slide the stick through the clamp until it balances on the knife-edge support, to locate the center of mass directly.

B. Center of Mass of Bar Located at Random Angle

1. Determine the mass of the bar.

2. Using three rod pulleys and right angle clamps, suspend the bar, with masses attached, at an angle between the supports, as shown in Figure 2. Measure all angles from the protractors attached to the bar. The angle for the bar is read from the protractor hanging freely downward. The distance d is measured from the lower end of the bar, to the point where the force is applied on the bar by the string.

Fig. 2

3. Find the location of the center of mass by solving the torque equation for dbar. As a check, balance the bar on the edge of a meter stick to find the center of mass.

C. Model Crane Boom

1. Measure the mass of the meter stick with a hole at one end, then balance it on the edge of another stick to determine the location of the center of mass, dstick.

2. Set up the apparatus as shown in Fig. 3 using the hooks and ledge of the chalkboard, and the meter stick with a hole at the upper end and its zero point at the lower end. Three small loops of string at the upper end can be used to attach m1 and the spring balances.

3. To find the compression on the meter stick, pull on spring balance #2 oriented parallel to the meter stick until the meter stick is just ready to pull away horizontally from the chalk ledge. The length d1 is also measured from the zero point of the ruler to the point

- 35 -

where the forces are applied to the stick. Record d1, , and the readings of both spring balances.

4. Calculate the tension T1, the theoretical reading of spring balance #1, from the torque equation. When the meter stick just starts to pull away horizontally from the chalk ledge, there is no horizontal force on the bottom of the meter stick. Use the force equation and your theoretical reading of T1 to calculate T2. Compare with the experimental values by computing the percent difference.

Fig. 3

- 36 -

Experiment 14

ARCHIMEDES' PRINCIPLE

INTRODUCTION

Archimedes' principle states that an object, partially or totally immersed in a fluid, is buoyed up by a force which is equal to the weight of the fluid which is displaced by the object. This experiment will make use of the principle of Archimedes in two ways: first, to verify that the principle is valid by determining densities of various solids with known densities; second, to use the principle to determine densities of various "unknown" solids and liquids.

- 37 -


Balance Vernier caliper Wooden sphereSupport rod, short Rock specimen Cylinders (Fe, Al, Cu)Hydrometer Lab jack Waterproof stringScissors Unknown fluid Graduated cylinder, 250 mlBeaker, 600 ml Table clamp Paper clip


Part A: Density of a Regularly-Shaped Object:

1. Place the balance on top of the support rod, clamped to your table. Turn the balance so the left side of the balance is over the table. Unbend a paper clip, and attach it to the bottom of the vertical shaft of the left balance pan, underneath the base. Set the balance to read zero, and rotate the calibration mass until the needle is zeroed.

2. Tie an aluminum cylinder with waterproof string to the paper clip. Determine the mass of the cylinder. Immerse the cylinder into a beaker of tap water and observe the apparent mass on the balance. All measurements of mass should be to the nearest tenth of a gram.

3. The density of water is 1.000 g/cm3. Compute the density of the cylinder using Archimedes' principle, which is given by the following equation:

object = fluid

Compare your measured value with the accepted value by computing the percent difference. As an alternate check, compute the density directly using the mass of the object and the volume calculated from the dimensions of the object. In this case, the volume of a solid cylinder of diameter d and length l is d2l /4, and the density is given by the following equation:

object =

4. Repeat steps 2 and 3 for the other two cylinders.

Part B: Density of an Object that Floats in Water:

1. Determine the mass M of an object such as a wooden sphere that can float on water. Use one of the cylinders as a sinker. Tie the sinker to the wooden sphere.

2. Observe the apparent mass, M with the wooden sphere out of the water and the sinker in the water (be certain the sinker isn't touching the bottom). Then observe the

- 38 -

mass of object in airmass of object in air – apparent mass of object in fluid

mass of objectvolume of object

.

.

apparent mass, M with both submerged and suspended. From these data, compute the density using the following equation:

object = fluid

That is,

object = fluid M

M ' − M ' '

Part C: Density of an Irregularly-shaped Object:

1. Find the density of a rock using Archimedes' principle, as performed in Part A.

Part D: Density of a Fluid:

1. Observe the apparent mass of the aluminum cylinder in the unknown fluid poured into the beaker. Use this value, the mass of the aluminum cylinder in air and the accepted value of its density to calculate the density of the unknown fluid fluid from Archimedes’ Principle (the equation in step 3 of Part A).

2. Pour the unknown fluid from the beaker into the cylinder. Use a hydrometer to find the density of the unknown fluid directly, making sure that the hydrometer does not touch bottom. Read the scale that starts at 1.000. When finished, remove the paper clip from the bottom of the scale, return the unknown fluid to its container, and thoroughly wash and dry all glassware.

Experiment 15

BOYLE'S LAW

INTRODUCTION

The purpose of this experiment is to observe the relationship between the pressure and the volume of a gas (air), when the amount of gas and the temperature of the gas are kept constant. The relationship between these two quantities is known as Boyle's law:

PV = c ,

where P is the total pressure in Newtons per meter squared, V is the volume in meters - 39 -

mass of woodapparent mass, sinker in water, wood out – apparent mass, sinker and wood in water

.

cubed; and c is a constant for a particular quantity of gas at a fixed temperature.Furthermore, the gas constant, R, can be calculated using the ideal gas law:

PV = nRT,

where n is the number of moles and R is the gas constant in Joules / moleKelvin. The method that will be used to verify Boyle's law is to directly vary the pressure on

a column of gas enclosed by a cylinder and piston, and then read the resulting volume.


Boyle's law apparatus Thermometer, 0–100oC Buret clampClear plastic triangle 0.5, 1 and 2-kg masses Ring stand1 sheet of graph paper


1. Set up the apparatus as shown in Figure 1, using the buret clamp and ring stand to hold the cylinder securely. Tighten the clamp enough to hold the cylinder in position, without squeezing it. Be careful at all times to keep the masses from falling on your feet.

Fig. 1.

2. Push the wooden block onto the piston and wet the piston with water in order to lubricate it. Place a string in the cylinder and insert the piston. Set the piston at the 35.0-cm3 mark and pull the string out; this will be your initial volume of gas at atmospheric pressure. The total pressure in the Boyle’s law equation is the applied pressure plus the atmospheric pressure. Use the value of 101,000 N/m2 for the atmospheric pressure.

3. Start adding masses in 0.5-kg increments from 0.5 kg to 3.5 kg, reading the volume to the nearest tenth of a cm3 after each addition. To assure that the piston is not bound by friction, twist it gently and lift it slightly above the rest position each time. Then release and read the scale where the piston comes to rest. Repeat but twist and compress the piston slightly below the rest position, then release and read the scale. The average of the two readings is the volume.

4. Pressure is defined as force per unit area, and the cross-sectional area of the cylinder is 0.000452 m2.

- 40 -

Applied pressure =

ForceArea =

Mass ( in kg )∗ 9 .80 ( in m /s2 )0 .000452 ( in m2 )

P = Total pressure = Applied pressure + 101,000 N/m2

5. Calculate c = PV for each set of P-V values and enter these in your data table. Calculate an average value of c and enter this in your data table.

6. Plot total pressure P in Newtons/meter2 on the vertical axis vs. the reciprocal of the volume 1/V in meters-3 on the horizontal axis of a sheet of graph paper, and draw the best straight line through the points. A straight-line graph will demonstrate the validity of Boyle's law. Choose the scale of each axis carefully, so the data spreads out over most of the graph. Each axis should be labeled by the quantity it represents, with its units in brackets. The graph should be given a label that describes the physical arrangement that generated the data.

7. In the ideal gas law PV = nRT, “n” is the number of moles of gas, indicating how much gas is present (n times 6.02 X 1023 is the number of particles of gas). In a warm room, gas expands and the number of moles in 35.0 cm3 decreases. Measure the room temperature in oC. The ideal gas law uses temperature measured in Kelvin degrees, which is the Celsius temperature plus 273.15. Calculate T.

8. The number of moles in a 35.0-cm3 cylinder at one atmosphere of pressure is

n = 0.42640

T . Calculate the number of moles of air used in your experiment.

9. You can now use the ideal gas law to calculate a value for the gas constant, from R = c/nT, where c is your average value of the constant c. Calculate your value of R and compute its percent difference from the given value of 8.315 J/molK accepted by the scientific community.

Experiment 16

HEAT OF FUSION OF ICE

INTRODUCTION

When one gram of ice at standard pressure undergoes the phase change from ice to water, it absorbs a certain amount of heat energy needed for the creation of the more random molecular arrangement in water (crystals vs. a liquid), and this amount of heat is known as the latent heat of fusion Lf. The word latent means “hidden”. The usage stems from the fact that during a phase change the temperature of the substance doesn’t change as the substance is absorbing heat.

In this experiment the latent heat of fusion of ice will be determined by using the method of mixtures and applying the conservation of energy, that is, the heat lost is equal

- 41 -

to the heat gained.An ice cube placed into a measured amount of warmed water is melted, cooling the

water in the process. By observing the various temperatures before mixing, T i, and after mixing, Tf, the heat of fusion may be calculated as follows:

HEAT LOST (in calories):

by water = (mass of water in grams)(1 cal/gramoC)(Ti - Tf)by calorimeter = (mass of calorimeter in grams)(0.22 cal/gramoC)(Ti - Tf)

HEAT GAINED (in calories):

by melting ice cube due to phase change = (mass of ice cube in grams) Lfby ice cube after melting = (mass of ice cube in grams)(1 cal/gramoC))(Tf - 0oC)

So, from the law of conservation of energy,

Heat gained by melting ice = heat lost by water + heat lost by calorimeter

heat gained by ice cube after melting

HEAT OF FUSION (in calories/gram):

Lf =


Double wall calorimeter Electric steam generator GlycerinBalance Ice cubes (in ice water) ForcepsCounter weight masses Thermometer 600 ml BeakerDewar flask


1. In a beaker, mix some of the hot water from the steam generator with cold tap water until a temperature of about 40oC is reached.

2. Determine the mass of the inner cup plus stirrer of the calorimeter (without the fiber collar).

3. Fill the inner calorimeter cup about two-thirds full of the warmed water from step 1 and then determine the mass of the cup, stirrer and water combination. The difference between the mass measured in step 2 and step 3 is the mass of the water.

4. Replace the fiber collar on the inner cup and carefully place inner cup and water into the outer jacket. Cover with the plastic disk, place the thermometer through the central hole and place the stirrer through the hole beside it. Record the initial temperature, T i. Place the ice cube into the water after wiping it with a paper towel.

- 42 -

heat absorbed due to phase change of melting icemass of ice

5. Stir the mixture carefully, being careful not to break the thermometer. When the ice cube has just melted, record the final temperature, Tf.

6. Determine the mass of the cup, stirrer and contents. The difference between this mass and that of step 3 is the mass of the ice cube.

7. Add the heat lost by the water and by the calorimeter, and subtract the heat gained by the ice cube after it has melted. The result must be the heat gained by the ice cube as it was melting. Divide this by the mass of the ice to get the heat of fusion of the ice.

8. Repeat this procedure two more times and average three suitable values. The accepted value for the heat of fusion of ice is 79.6 cal/gram.

9. Before leaving, thoroughly dry your equipment with paper towels.

Experiment 17

HEAT OF VAPORIZATION OF WATER

INTRODUCTION

When a substance undergoes a phase change from a liquid to a gas, the heat energy goes into doing work against intermolecular forces. This heat energy is called latent (hidden) since no temperature change is seen during the process. The accepted value of the latent heat of vaporization of water is 540 cal/gram.

In this experiment we will use the calorimetry method of mixtures, or heat gained is

- 43 -

equal to heat lost, to obtain a value for this latent heat. From conservation of energy, and assuming negligible heat loss or gain to the surroundings, we can write an equation for our system:

HEAT GAINED: BY THE COOL WATER + CALORIMETER CUP AND STIRRER = HEAT LOST: BY CONDENSING STEAM + HOT CONDENSED WATER,

or symbolically: Qcool water + Qcup and stirrer= Qcondensing steam + Qhot water

so: Qcondensing steam = Qcool water + Qcup and stirrer - Qhot water

where Qcool water = mwcw (Tf - Ti)Qcup and stirrer = mcsccs (Tf - Ti) andQhot water = mscw (100oC - Tf) .

The m's and c's are masses and specific heats respectively, Tf is the final temperature, and Ti is the initial temperature of the cup contents and stirrer. The subscripts s, v, w, and cs stand for steam, vaporization, water, and cup/stirrer, respectively. The specific heat of water is cw = 1.00 cal/gramoC, and the specific heat of the aluminum cup and stirrer is ccs = 0.22 cal/gramoC.

The latent heat of vaporization, Lv, is the amount of heat released by one gram of steam at 100oC as it condenses to become one gram of liquid water at 100oC.


Double wall calorimeter Thermometer GlycerinElectric steam generator Water trap assembly BalanceCounter weight masses 600 ml Beaker Pinch clampDouble pan balance Dewar flask Ice


1. Set up the steam generator, water trap and calorimeter as indicated in Figure 1. Do not insert the steam line (the glass tube) into the calorimeter as yet. Fill the boiler half-full with water and begin to heat it. The water trap is used to prevent condensed water from entering the calorimeter.

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Fig. 1.

2. Determine the mass of the inner cup plus stirrer of the calorimeter (without the fiber collar).

3. Fill the inner cup of the calorimeter about two-thirds full of water. Cool the water to about 15oC below ambient temperature with ice. Weigh and record the mass of the inner calorimeter cup, stirrer and cooled water. Gently stir and make sure that all the ice has melted and record the initial temperature Ti. Immediately do the next step.

4. The water in the boiler should be boiling freely by now. Place the fiber collar and inner cup inside the calorimeter, and cap it with the thermometer in the center, touching the water. Introduce the steam tube into the calorimeter water by lifting up and carefully lowering the steam generator and water trap together, then stir continually. Open the pinch clamp occasionally to drain any water that collects in the water trap into your sink. When the temperature is about 15oC above ambient temperature, turn off the boiler and wait for the steam to stop entering the water trap. Remove the steam tube, gently stir and record the final temperature Tf.

5. Reweigh the inner cup, stirrer, water and condensed steam in order to determine the mass of the condensed steam.

6. Calculate Qcool water, Qcup and stirrer, Qhot water and Qcondensing steam.

7. In the previous step, you calculated Qcondensing steam. Because this equals msLv, you can divide Qcondensing steam by ms to get the latent heat of vaporization, Lv.

8. Repeat this experiment twice to get an average value of Lv. Compare this average value to the accepted value of 540 cal/gram by computing the percent difference.


Experiment 18

SPECIFIC HEAT OF METALS- 45 -

INTRODUCTION

In this experiment the specific heat of two metals (copper and lead) will be determined by the method of mixtures; heat lost is equal to heat gained. The increase in temperature of chilled water and the decrease in temperature of the heated metal will be used to calculate the specific heat of the metal.


Electric steam generator Ice cubes BalanceCopper shot Specimen holder Mallet Double wall calorimeter Vernier caliper Lead shotTwo 100 oC thermometers 600 ml beaker Flint strikerCopper cylinder Bunsen burner Forceps


Part A: Specific Heats of Copper and Lead.

1. Fill the steam generator three-quarters full of water and start heating it.

2. Determine the mass of the empty specimen holder, to the nearest tenth of a gram, and record this on the data sheet. Fill the specimen holder one-third full of copper shot, determine this mass, and calculate the mass of the shot alone.

3. Bury the bottom of the thermometer in the copper shot inside the specimen holder, and suspend the specimen holder in the heating water.

4. Weigh the inner cup and stirrer of the calorimeter (without the fiber collar). Pour into the cup enough chilled water (10oC below room temperature) to make it one-third full. If the water is not cool enough, add some ice and wait for the ice to melt. Then weigh the inner cup, stirrer and water, and calculate the mass of the water alone. Place the cup, stirrer and fiber collar into the outer cup. Cover with the lid. Place the thermometer into the calorimeter through the central hole in the lid to record the initial temperature of the water and the aluminum. Try to measure the temperatures in this lab to the nearest tenth of a degree.

5. When the shot is heated to a temperature greater than 90oC, record the temperature, then carefully remove the shot and cup from the steam generator. Carefully pour the shot (no splashing, and do not break the thermometer) into the inner calorimeter cup, and replace the lid.

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6. Stir the contents of the cup. Record the highest temperature reached on the thermometer.

7. When you are finished with the shot, spread it out on a paper towel to dry, then return it to its container.

8. Repeat the entire procedure using the lead shot.

9. The heat gained by the water in calories is Q = m X c X T:

heat gained = (mass of water) X (specific heat of water) X (temperature change).

The specific heat of water is 1.00 cal/goC.

The heat gained by the aluminum calorimeter in calories is:

(mass of calorimeter) X (specific heat of aluminum) X (temperature change).

The specific heat of aluminum is 0.22 cal/goC.

The calorimeter (inner cup and stirrer) went through the same temperature change as the water.

The heat lost by the shot must equal the heat gained by the cool water and the calorimeter, according to the law of the conservation of energy.

The specific heat of the shot is:

c = Qm × ΔT

=(heat lost )

(mass of shot ) x ( temperature change of shot ) .

10.Compare your experimental values of the specific heat with the accepted value by computing the percent difference. The specific heat of lead is 0.031 cal/goC and 0.093 cal/goC for copper.

Part B: Estimating The Temperature of a Bunsen Burner Flame.

1. Determine the mass of your copper cylinder. As in the previous part of the experiment, add chilled water to the inner cup of the calorimeter so that it is about one-third full. Determine the mass of this chilled water.

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2. Put the inner cup into the calorimeter and insert a thermometer through the lid.

3. Connect the Bunsen burner base to the methane tap above your sink, turn the gas flow on, and light the top of the burner by creating sparks with the flint striker. If necessary, strike the tap with the mallet to dislodge obstructions to the gas flow. Adjust the air flow at the bottom of the burner to get a hot flame. Warning! Keep the flame away from all flammable objects.

4. Hold a copper cylinder with forceps directly in the hottest part of a bunsen burner flame for about 2 minutes. Record the temperature of the chilled water. Quickly transfer the cylinder to the inner calorimeter cup, then turn off the gas flow to the Bunsen burner.

5. Record the highest final temperature reached, while stirring the water with the stirrer.

6. Determine the initial temperature of the copper cylinder, using the accepted value of

the specific heat of copper, T =

Qm × c and Tinitial = Tfinal + T. The initial

temperature should approximately equal the temperature of the flame.

7. Dry all equipment thoroughly before handing in your lab work. Be sure that your gas taps are turned all the way off.

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Experiment 19

THE COEFFICIENT OF LINEAR EXPANSION

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INTRODUCTION

With rare exceptions, when materials are heated or cooled they undergo expansion or contraction respectively. From the standpoint of materials science, this process must be taken into account when designing structures that are subjected to temperature variations. Otherwise, tensile or compressive stresses might develop which would destroy the structure.

The coefficient of linear (one-dimensional) expansion is defined as the fractional increase in length divided by the temperature change. The coefficient is found to be almost constant over a large range of temperatures. If we call this coefficient alpha, the definition can be stated mathematically as follows:

=

ΔL/LΔT

where L is the change in length, L is the original length, and T is the temperature change in Celsius degrees.

In this experiment, we will determine the value of the coefficient of linear expansion of several common metals. The length of the metal rod is measured at room temperature, then steam is passed over the rod, causing it to expand. The amount of expansion is then measured with a dial indicator. The coefficient of linear expansion can then be determined using the data gathered.


Expansion apparatus Electric steam generator Meter StickThermometer Glycerin Dial indicatorRubber tubing Metal rods (Cu, Al, Fe)


1. Measure the length of the rod carefully to the nearest millimeter and record this length, L. Determine the ambient (room) temperature and record it on the data sheet.

2. Set up the apparatus as shown in Figure 1. The steam jacket for the rod has openings for steam, water, thermometer, and rod ends. Dab the bottom of the thermometer with glycerin if it does not slide smoothly through the stopper. Be careful not to shatter the thermometer against the metal rod. Fill the steam generator two-thirds full with water and start to heat it, but do not connect the steam line to the apparatus yet. Insert the rod into the apparatus and make careful contact with the dial indicator by screwing in the caliper so the dial indicator’s dial advances as the caliper is turned. You can unscrew the clamp and rotate the black plastic outer dial, to zero the dial indicator.

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Fig. 1. Linear Expansion Apparatus with Associated Equipment

3. When the steam generator is producing steam briskly, connect the steam tube to the inlet on the apparatus. Warning! Do not get scalded or burned by the steam or the steam generator.

4. After several minutes have passed, the temperature will be near 100oC and the dial indicator will have a constant reading. Record both values. L will equal the final reading of the dial indicator minus the initial reading. Remove the black rubber top from the steam generator to permit the apparatus to cool between experiments. Use paper towels to insulate your hands while removing the top.

5. Compute the coefficient of linear expansion and record it on the data sheet. Compare your values to the known values by computing the percent difference.

6. Repeat the above procedure for the other two rods.


Fig. 2. Dial indicator

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P11 Lab Manual-Morris - Los Angeles Harbor College Lab Book Pt1.docx · Web viewTHE PHYSICS 11 LAB BOOK Book 1: Labs 1 – 19. TABLE OF CONTENTS MECHANICS AND PROPERTIES OF MATTER