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Department of Science, Engineering and Architecture. Division of Business, Math, Science, Technology (BMST) BMST AVP: Stacey Moegenburg LRC 221
PHY 101 - General Physics l
PHY 101: General Physics I
LAB
Professor: Michael Morgante, BSCE, MEE, P.E.
[email protected] (845) 497-4000 ext. 311
2
Physics Lab Reports
Most lab reports in College Physics will be informal reports written by hand in a laboratory research book. There will be an occasional formal typed lab report required as well. This is an outline of the sections in a typical lab report. Title: Short and precise; should accurately depict experiment done. Abstract (do only for formal typed reports): A one paragraph concise summary of the experiment. Purpose: Give a rational explanation as to why you are conducting the experiment. Hypothesis: State your hypothesis. This should be an educated guess as to what you believe your investigation will show. Theoretical Background: Provide a summary of the relationships, including mathematical equations, which are relevant to the experiment. Materials and Equipment Provide a concise list of any materials and equipment that is needed to carry out the experiment. Procedure Give a detailed step-by-step description of how this experiment was conducted. Another scientist should be able to perform your lab using your method. Data collected
Data table (Produce a labeled table of your results, including units of measurements).
Calculations – show any calculations that you used in the interpretation o your data.
Graphs – provide any labeled with units, suitably scaled graphs to help with the data you collected.
Diagrams – provide relevant diagrams, correctly labeled. It is especially important to include force diagrams if appropriate.
Analysis
Summarize data trends – give a brief explanation of the observations, trends/links in the results.
Explain how errors could have occurred during the experiment and what steps could be taken to minimize their effects. If necessary, provide a statistical analysis of the accuracy of your data. Please avoid using the term “human error”, which is imprecise and lacking in specificity.
Conclusion Give a full explanation of the outcome of your experiment, noting if the purpose was fulfilled using this procedure. Was your hypothesis validated – why or why not? Explain concisely what you achieved by performing this experiment. Reflect on what this experiment did to further your knowledge either scientifically or personally. Include suggestions for further investigation.
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Example Lab Report
Newton‟s Second Law Joe Physics 1st Period
Hypothesis
Newton‟s Second Law can be used to describe the motion of a cart that is accelerated on a low-friction cart track by a hanging mass.
Theory Newton‟s Second Law is summarized by the equation F = ma, where F is the net
force on a system in Newtons, m is the total mass of the system in kg, and a is the acceleration in m/s2. If this law holds, then x = xo + vot + ½ at2, where x and xo are the final and initial positions, respectively, t is the time, vo the initial velocity, and a the
acceleration. If the cart is released from rest, the equation simplifies to x = xo + ½ at2.
Equipment
cart track cart mass hanger masses Pasco Science Workshop 500 pulley
laptop computer string motion sensor magazines (to level cart track)
Procedure 1. Level cart track with magazines. Do this by setting cart in center of track and placing magazines under one end or the other until cart does not roll by itself.
2. Place pulley on one end of the cart track. 3. Place cart on track. Connect cart to mass hanger with a string. The string must
be of a length appropriate to go over the pulley, and must allow the mass hanger to reach all the way to the floor. A length of about 1.2 m is good. 4. Set up the Pasco Science Workshop 500 and the laptop computer as
established in prior experiments. Attach the motion sensor to an analog port of the 500. 5. Measure the mass of the cart.
6. Put 50 g of mass on mass hanger, drape string over pulley, and hold cart so that it does not move. The mass hanger should be suspended well above the ground.
7. Start collecting position data with the motion sensor. 8. Release the cart, and allow it to accelerate down the ramp.
Cart track
Cart
Mass hanger
Pulley String
Motion sensor
Pasco 500 Computer
4
Position vs Time
x = 0.2806t2 + 0.0025t
R2 = 0.999
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.0 0.1 0.2 0.3 0.4 0.5
time (s)
po
sit
ion
(m
)
measured position
predicted position
Poly. (measuredposition)
Data Cart mass: 500 g
Hanging mass: 50 g
Analysis
The data can be shown to best be fit by an equation of the form x = xo + vot + ½ (0.654) t2, which suggests constant acceleration. The exact equation deviates somewhat from the theoretical equation, in which the acceleration is 0.654 m/s2, as determined by
the Newton‟s Laws analysis of the experimental setup. However, agreement is close enough to verify the suitability of Newton‟s Second Law to the experimental situation.
Results
Data point time measured position predicted position1 0.000 0.000 0.000
2 0.100 0.004 0.003
3 0.200 0.011 0.013
4 0.300 0.026 0.029
5 0.400 0.046 0.052
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The hypothesis has been verified. Newton‟s Second Law is predictive of behavior of a cart on a low-friction cart track when the cart is accelerated by a hanging mass.
Conclusion or Discussion
It is apparent that Newton‟s Second Law is predictive, but does not provide an
exact fit of the experimental data. Certain problems have been ignored; among these are the rotational inertia of the pulley and the friction of the pulley with its axle, the friction of the cart‟s wheels on their axles, and possibly the resistance of the air as the mass falls
and the cart accelerates. It is possible that even closer agreement between theory and experiment could be achieved if rotational inertia of the pulley, and its impact on
acceleration, were considered. Also, more trials could have been performed had time permitted this.
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Lab Rubric A. Criteria: Designs Experiment Student demonstrates knowledge and skills necessary to perform scientific inquiry.
Standards and Benchmarks: SC11.3.1; SC11.3.2; SC11.8.4; and SC11.l.X
Level 4 Level 3 Level 2 Level 1
The experimental design meets all requirements of
a Level 3, AND
Considers current research and
understanding of the question being addressed.
The experimental design includes:
An hypothesis with cause/effect relationship which
addresses the question being studied;
Choice of controls
Consideration of sample
Observations and/or
measurements that are
sufficient to address the question being asked and are reproducible
A description of the
procedures and materials to be used.
All aspects of the experimental design are logically related to each other, to provide a
defensible experiment.
The experimental design is incomplete, but the design is
sufficient for providing information on the question being asked.
(Check all elements missing or incomplete.)
An hypothesis with
cause/effect relationship which addresses the question being studied
Choice of controls
Consideration of sample size
Observations and/or
measurements that are sufficient to address the question being asked and
are reproducible
A description of the
procedures and materials to be used.
The experiment is completed without an
explanation of the design;
OR Design is inadequate
for answering any aspects of the question;
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B. Criteria: Conducts the Experiment Student demonstrates knowledge and skills necessary to perform scientific inquiry. Standards and Benchmarks: SCI 1.3.1; 11.3.2;
SCI 1.8.4; and SCI 1.1.X
Level 4 Level 3 Level 2 Level 1
Meets all of Level 3 requirements;
AND Based upon findings
from the original experiment, there is evidence that an
experiment was conducted to address a new question directly
linked to the findings of the original question;
OR
An additional and related experiment is conducted
to further extend understanding
and/or to implement a modified experimental design.
OR A new experimental
design is proposed that exhibits deeper
understanding of concepts and/or extends
thinking beyond original conclusions.
The experiment was implemented, including:
Appropriate
observations and/or
measurements collected using consistent
methods so that measurements are repeatable.
Controls
implemented to examine one variable at a
time. AND
Any explanations in changes of the
design that address the original question
are documented
with appropriate observations and/or measurements.
Relevant observations and/or measurements are missing or are not defensible;
OR
Controls were not implemented to examine one variable at a time;
The experiment was attempted but is incomplete.
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C. Criteria: Representation - Tables, graphs, models, diagrams, or other appropriate representations. Student uses representations to communicate and apply
scientific concepts, in lab reports and technical writing.
Standards and Benchmarks: SCI 1.5.2; SCI 1.5.3
Level 4 Level 3 Level 2 Level 1
Representations are accurate and appropriate,
meeting requirements of Level 3, and
include other elements, such as:
Data set is
displayed in multiple ways to
provide additional information
or a different perspective
Data is
represented
multiple ways to make a point
Data is
represented multiple ways to
show a trend
Additional
representation(s) used
to explain a concept, solve a
problem, or as an extension of
the situation.
Any tables, graphs, models, or diagrams are appropriate for
representing the observations,
measurements, or concepts. There may be some flaws, but the flaws do not negatively impact the
understanding or use of the data, diagram, model, etc. Conventions of representation to
consider:
Data tables have accurate
titles, correct values, and labels
Graphs have appropriate titles;
correct scaling; independent and dependent variables labeled correctly; and values
accurately plotted.
Models and diagrams are
labeled.
Tables, graphs, models, or diagrams used have a significant flaw(s) that
negatively impacts the understanding or use of the representation, such as:
Data is collected in tables,
but not organized or correctly labeled and titled
The graph selected is not
appropriate for representing the situation
Graphs contain errors or
inconsistencies in scaling, labeling, or plotting
The diagram or model is
unclear (no labels, titles, explanation).
.
An attempt is made to organize or graph data (observations and/or
measurements), or to use a diagram or model, but the
representation chosen cannot be used to effectively
communicate the concept for the given situation;
OR
Tables, graphs, diagrams, or models
are missing or have errors in the conventions
throughout;
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D. Criteria: Conclusions - Student demonstrates knowledge and skills necessary to perform scientific inquiry.
Standards and Benchmarks: SCI 1.3.1; SCI 1.3.2; SCI 1.3.3; and SC11.1.X
Level 4 Level 3 Level 2 Level 1
Meets all
requirements of Level 3:
AND Demonstrates an in-
depth understanding or extensive knowledge of the
concepts by using the conclusions to do any of the
following:
make further
predictions
ask/address
additional questions
generalize
scientific
concepts
provide scientific
explanations of question studied
or an application related to the findings compare
the conclusion to other research and models and
appropriately address deficiencies.
Conclusions drawn address
the hypothesis and are supported with relevant observations or
measurements. All aspects of the experiment are addressed.
AND
If applicable, results are evaluated to determine if they are reasonable and
there is evidence that an attempt was made to determine the source of
error.
Conclusions drawn address the
hypothesis, but are not fully or consistently supported by observations and/or
measurements; OR
Observations and measurements are summarized, but no
conclusion s are drawn; OR
Not all elements of the experiment are addressed in the
conclusions;
OR Observations and measurements
are used to support the conclusions, but the observations and measurements may be
inappropriate.
Conclusions drawn do
not address the hypothesis;
OR Conclusions drawn
address hypothesis, but are inconsistent or in conflict with observations
and measurements.
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F. Criteria: Communicates Results Student communicates and applies scientific principles. (Note: This criterion assesses communication, not conceptual understanding.)
Standards and Benchmarks: SCI 1.5.3 and SCI 1. 5.2
Level 4 Level 3 Level 2 Level 1
Meets requirements of Level 3,
AND Explanations are
strengthened by the use of such things as:
Graphic
organizers
Diagrams
A keying system
Cross-referencing
Additional Tables,
Models, Graphs
Scientific terms are accurately and appropriately applied in
report. The application of
grammar and conventions do not get in the way of understanding the results
of the experiment.
Inconsistent use of accurate and appropriate scientific terms throughout the report.
The application of grammar and conventions get in the
way of completely understanding the experiment or results.
Scientific vocabulary used, but inaccurate throughout the report or not used when
the opportunity exists; OR
Used common terms instead of appropriate scientific
terminology. The application of grammar
and conventions make it hard to follow the explanations and/or the
results of the experiment.
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Graphing using Excel The following values for Time and Height were obtained during a field
test of a new SUNY Orange Rocket. These data were obtained using onboard digital timers and an altimeter which sampled the height every second for ten seconds.
Data entry and computations using Excel.
1. Open Excel and enter the original Time and Height data into the A and B columns of the worksheet. When possible always enter the original data in the original units used
during the experiment. Any conversion of the units should be done in Excel so that a record of the manipulation exists. 2. Convert the original data to [mks] units. To have Excel do this computation start cell
C2 with an equal sign followed by the equation: =B2*1000 and hit enter. 3. To copy this equation to the rest of the cells below, hold the cursor over the lower right corner of the cell C2 containing the equation and „click and drag‟ the equation down. 4. In column D calculate the average speed of the rocket using the equation Vavg=d/t.
Or: =C2/A2 5. Since the rocket started from rest the final velocity should be twice the average velocity*. Calculate the final velocity (Vf) in column E. Copy down to complete the entire
table. *Note: This assumes that the rocket experienced constant acceleration during the flight.
Making graphs (charts) using Excel. 6. Make a graph of Height vs Time.
Click and drag down column A highlighting the cells, then holding the Ctrl key click and drag down any other column in this case C. Y
Note: Excel always designates the leftmost column as the X variable, as in: (X,Y).
X
A B C D E 1 Time
[sec]
Height
[km]
Height
[m]
Vavg = H/T
[m/s]
Vf = 2* Vavg
[m/s]
2 1 0.05 50 50 100
3 2 0.20 -
4 3 0.50 -
5 4 0.80 -
6 5 1.20 -
7 6 2.00 -
8 7 2.40 -
9 8 3.00 -
10 9 4.00 -
11 10 5.00 -
H
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7. At the top of the screen select Insert followed by Scatter, followed by the chart icon with no lines. You should now see a preview of your graph. At the top of the screen select the leftmost Chart Layout option. This will format the
graph for Axis labels and a Title.
Now is the time to check that X is Time and Y is Height.
If it is not: You can redo the graph after switching the data columns around (or copying
some extra columns to the right for graphing purposes). Or you can click on the Select Data icon (at
top) followed by Edit in the window and manually switch the X and Y values designations. In this case, by making the A‟s
into C‟s and making the C‟s into A‟s. Annoying but you don‟t lose your equations and Titles.
You can also add Axis Titles or Labels at any time by selecting Layout under Chart Tools:
8. To add a Trendline: Right click on any data point and they should all light up.
Select: Add Trendline from the pull down menu.
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10. Select a Linear trendine. Also select Display Equation on chart and
Display R-squared on chart**. ** R2 is a Regression statistic that indicates how well an equation fits the data.
A perfect correlation has an R2 = 1.000 An R2 below 0.90 is considered to be a weak or poor correlation. In that case a Power or
polynomial equation may be a better choice.
Hit Close to add the Trendline. You may repeat these steps and add as many Trendlines to a graph as you need.
Make the following three Graphs:
1. Height vs. Time 2. Final Velocity vs. Time 3. Final Velocity vs. Height
H Vf Vf
T T H Insert Linear and Power fit equations on each graph.
Label each axis including units. Give each graph a Title. (NOT: Dist vs. Time)! For example: “Rocket Altitude Test” or “Rocket Velocity Test” or whatever you like just
not (Y vs. X)! Questions:
Graph 1: Height vs. Time: Which equation is the better fit (Comment on the regression values)? What kinematic equation do you think the Power fit represents?
Graph 2: Vf vs. Time: Which equation is the better fit?
Linear slope = _____________ What do you think the linear slope represents (check the units)?
What kinematic equation do you think the linear fit represents?
Graph 3: Vf vs. Height: Which equation is the better fit? What kinematic equation do you think the power fit represents?
Optional: At five kilometers the engine suddenly shut down.
i. How high does the rocket ultimately go, [Assume a = g and ignore air resistance]? ii. How long until it hits the ground ( if the parachute does not open)?
Iii. How fast is it going when it crashes?
14
MEASUREMENT AND GRAPHICAL ANALYSIS In this experiment the relationship between the mass and the radius of various steel
spheres will be examined. The use of a dial caliper and computer analysis of data will be emphasized.
Theory: Density ( ρ=„rho‟) is defined as mass per unit volume: = M/V. A series of objects made from the same material should all have the same density.
We will be analyzing steel spheres whose Volume is 4/3r3. Combining the above equations yields our theory for mass vs. radius:
M = [4/3] r 3
We will use various graphs to prove or support this hypothesis. According to the equation Mass should be related to radius cubed. A Power fit equation (y=A xn) should provide a direct match for the theory. Compare the power (n) and solve for the density
(ρ) by setting the coefficient term (A) from excel equal to 4/3. Any equation can be linearized by including the power as part of the axis variable ie: let x = r2, or x = r3. The best fitting linear graph then supports the hypothesis. Any poor
fitting graphs are still useful as they omit opposing hypotheses. Our basic hypothesis states that: mass is proportional to radius cubed, let‟s prove it.
Method: 1. Using the dial caliper or the micrometer measure the diameter of each sphere along
three axis and compute the average radius for each sphere.
2. Determine the mass of each sphere using a scale.
3. Construct a data table on the computer: r, r2, r3, M, Vol , i.. On the data table compare the density ρ for each sphere. Does it vary?
Compute the average of these densities 1 =average(A1:A6) ii. Develop the following three graphs. Each plot must be fully labeled, show the equation of the trendline and include the statistical regression value „R2‟. This regression statistic indicates a good fit of the equation to the data if it = to 1.
a. Plot Mass [M] vs. radius[r]: (Power fit) and (Linear fit) with equations. b. Plot M vs r2. (Linear fit). Linearized test for squared relationship. M c. Plot M vs r3. (Linear fit). Linearized test for cubic relationship.
4. Which graphs best represent the theory: M = 4/3r3 , which don‟t? r, r2, r3
5. The constant (A) in the power fit equation from graph a is equal to 4/3 set
these equal and solve for 2. How does it compare to the actual density of steel? How does the power of your equation relate to the power of the theoretical equation?
6. Use the slopes from the Linearized graphs to find the average density 3 and 4
in the same manner.
7. Find the percent deviation of these values using: % Deviation = Your Value- Accepted Value X 100
Accepted Value
(Keep this equation handy we will be using it often during the semester). 8. Compare the calculated densities with the accepted and create a table
summarizing your results. Include % deviations. Note: steel = 0.0078g/mm3 =7,800 kg/m3
15
Trajectory of a Horizontally Launched Projectile
Purpose: To collect, tabulate, plot, and analyze data for a horizontally launched projectile.
Theory: For any projectile, the horizontal distance traveled follows the equation
x = vxt
where vx is the horizontal velocity upon launch, and t is the time. The vertical
distance traveled follows the equation y = - ½ g t2
where g is the acceleration due to gravity (9.8 m/s2) and t is the time. Horizontal and
vertical displacements are independent of each other.
Equipment: Projectile (steel ball), launching ramp, carbon paper, graph paper, ruler. Procedure: Using the equipment given, come up with a method to reproducibly launch
the projectile horizontally with a consistent speed. After you have come up with a method to launch the projectile, come up with a procedure to record the distance the projectile falls (the dependent variable) as a function of the horizontal distance it travels
(the independent variable). Data and calculated results: Collect (x,y) data for at least six horizontal distances, and
do several trials at each distance to test the reproducibility of your method. Put the resulting (x,y) data in a table. Graph the data on an (x,y) graph. The resulting curve represents the trajectory of the projectile.
From the y values in the trajectory, estimate the time it takes for the projectile to reach
each (x,y) location. From those estimated times, calculate the horizontal speed of the projectile at each of the (x,y) points. Conclusion/Discussion: Should include some discussion of the following: What
difficulties did you experience in designing this experiment? Is the data reproducible for each (x,y) point? What are some possible errors? Does the horizontal speed of the
projectile seem constant for the entire trajectory? Does your trajectory support the theoretical equations shown above?
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Newton’s Second Law
Purpose: To examine how well Newton‟s Second Law describes a cart-and-pulley system “without” friction. To graph position, velocity, and acceleration as a function of time for a uniformly accelerating system.
Theory: Newton‟s Second Law describes the relationship between force, mass, and
acceleration
F = ma
where F is the resultant of the forces acting upon a system, m is the mass of the system and a is the acceleration. The acceleration should be uniform if the forces are
uniform, and should be applicable in the standard kinematic equations.
Equipment: Tape timer and ticker tape, carts and cart tracks, pulley, string, mass hanger and masses, tape, ring stand and clamps, meter sticks.
Procedure: Using the equipment provided at your lab station (including in the cabinet), devise a method to set a cart in motion using a uniform accelerating force. Measure the position as a function of time using the tape timer and ticker tape. (NOTE: The timer can
be set at 10 Hz or 40 Hz; select the most appropriate setting. 10 Hz makes 10 marks in one second; 40 Hz makes 40 marks in one second.)
After you design your experiment, you are expected to run it at least twice. Either the accelerating force or the mass of the system must be varied for your different trials.
Data and calculated results: You must include a diagram of your experimental setup. All data collected should appear in a data table that is complete enough that your
calculated results can be verified. Sample calculations should be shown. Results should be clearly indicated. Graphs of position, velocity, and acceleration as a function of time should be included for each trial.
Conclusion/Discussion: Should include some discussion of the following: How well
does Newton‟s Second Law predict your results when friction is ignored? How significant
is the roll of friction in this experiment? What are some experimental difficulties you encountered?
17
Atwood & Gravity Lab
Purpose:
To measure the acceleration of gravity using an Atwood‟s machine.
Description:
In order to slow down a falling object, we need to apply a force to the object in the
upward direction. This can be down using an Atwood‟s machine: two different masses
connected by a string over a pulley. For m2>m1, the acceleration is given by:
a = g (m2 –m1)/(m2 +m1)
By picking the value of the masses, we can tune the acceleration to a manageable
value (< 9.81 m/s2
) so that the elapsed times can be measured accurately by hand.
Using the elapsed time, we can calculate a and in turn, g.
Before you come to lab show that:
For m2>m1, the acceleration is given by:
a = g (m2 –m1)/(m2 +m1)
Draw a free body diagram of the Atwood machine setup and use Newton‟s 2nd law to
obtain the relation between a and g above. You can assume a massless and frictionless
pulley.
18
Equipment:
Computer, meter stick and stop watch, masses, and 50 g holder table clamp, long bar 3 ft, cross clamp, Atwood‟s machine pulley, string.
Procedure:
1. You should develop a data table to record your average time and calculated value for
g:
*Use masses so that the drop time is large enough that the issue of your reaction time is
minimized. Include your table in your report.
2. Set up your Atwood‟s machine: Mount the pulley is as high as possible. Tie one end of the string to mass 1 and tie the other end to mass 2. Hang the masses over the pulley then adjust the pulley height so that the bottom of the upper mass is 1.2-1.3 m above the
floor when the lower mass is on the floor.
Experiment: Pull the lighter side to the floor. Measure the time required for the heavier side to hit the floor. Drop the mass three times, and then repeat for
five mass pairs. Each drop should have its own row in the spreadsheet.
The displacement d and average elapsed time t are related by the following
kinematical equation d = 1/2 a t2
. Thus you can find an experimental from this
equation.
It is good experimental procedure to check the quality of your data as you go.
Have Excel calculate a value for g for every drop. If there are large deviations
from the expected value of g, discuss your experimental procedures with your lab
partner
Analysis:
Make a plot of your data with acceleration on the y axis and (m2-m1)/(m1 + m2) on the x
axis. Fit a line to these data. The slope should be the acceleration due to gravity, and the
intercept should be close to zero. You can also choose to set it to zero when you fit the
line. Include the plot in your report.
The slope of the line is one way to determine a value for g, and in most careful
experiments, it is the preferred method. Another way of determining g is to simply take
the mean of the values of g you have calculated at each trial. Does the difference
between the two values fall within the expected error bars? If the value from the slope
is much different that the "point values", this usually is a clue to a source of error.
Discussion of this is one of the things that should be found in your conclusion.
Use what you have learned so far to determine how accurate your results are.
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Conclusion: Compare your experiment value of g to the expected value. What sources
of errors may have affected your result? Also discuss the accuracy of your results and
comment on any points that deviate from the expected value.
*Testing reaction time
Before building your Atwood's machine, test your reaction time. Have one lab partner
hold a ruler and position the other to catch it. The second lab partner should grab the
ruler as quickly as possible after the first drops it. Measure the distance the ruler
dropped and use the following kinematical equation:
d = Vi + 1/2 a t2
Since Vi = 0 and a = g, this gives t = (2 d / g)0.5
Repeat this measurement several times to get an idea of your average reaction time.
Note that you can use the same general thinking to predict how long each trial of your
Atwood's Machine experiment will take. In this case, d is the distance that the mass
drops, and a will equal (m2-m1)/(m1 + m2)g. Pick your masses such that this time is large
enough that the issue of your reaction time is minimized.
20
Uniform Circular Motion Lab Purpose: To determine the force necessary to keep an object in circular motion (the centripetal force).
Instructions: Get a centripetal force apparatus.
Set up as shown in the diagram below.
Procedure:
a. Find the mass of the washers which are hanging at the end of the string, and the mass of the stopper. b. Have one lab group member carefully swing the stopper on the string
in a horizontal circle above his or her head. c. When the radius is constant (that is, the washers are not moving up or down),
and the period of rotation is consistent, have another lab group member find the
time for 10 revolutions. d. At the end of 10 revolutions, put your finger on the end of the tube to preserve
the radius at which the stopper on the end of the string was rotating. e. Measure the radius of the circle (the length of the string). f. Find the period, and then using the period and the radius, find the velocity of
the stopper as it rotates. g. Using the mass, velocity, and radius, calculate the centripetal force acting on the stopper. Should you use the mass of the stopper or the mass of the washers
in the equation for centripetal force?
h. Compare the value you measured for the centripetal force with the weight (not the mass) of the washers.
i. Repeat steps b through g for a different radius. j. Record all relevant data in a table, and answer the questions that follow: .
21
Analysis:
1. Briefly explain the relationship between the centripetal force and the amount of hanging weight.
2. Calculate the percent difference between the centripetal force and the hanging weight for each part of the lab. Show your work.
100% xshersWeightofWa
lForceCentripetashersWeightofWaDifference
3. In this lab, which quantities did you change and which quantities remained constant throughout the procedure of the lab?
4. How would the speed change if you shortened the period by half as long and
kept the radius constant? 5. How would the centripetal force be changed if you kept the mass and velocity
constant, but doubled the radius?
6. How would the centripetal force be changed if you kept the mass and radius
constant, but increased the speed by 3 times? Draw a free body diagram for your experiment. Plot the force on the string vs. the speed
of the stopper; draw a separate plot for each radius. (Hint: To find the speed of the stopper, you have to find the distance it travels and divide it by the time it takes. What is the distance the stopper travels if it is moving in a circle?)
Using Excel determine an equation for this line. Use this equation and the information you recorded to determine an expression for centripetal force.
Force
from the
hanging
washers
(N)
Stopper Speed (m/s)
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Conservation of Energy: The Inclined Plane
Purpose: To determine the work done on an object on an incline plane and to verify the law of the conservation of energy. Background: In the absence of friction, the work done to pull an object up an incline plane is equal to the work done to lift the object up the same vertical distance. That is, the change in gravitational potential energy is independent of the path taken to get to the height. When lifting an object straight up, work is only done against gravity. The work done by the moving force is equal to the change in gravitational potential energy if the object is moving at a constant speed. In order to move an object up an inclined plane, work must be done against the gravitational force AND friction on the inclined plane. The work done by the pulling force will be equal to the negative work done by friction, if the object is moving at a constant speed. Materials: Inclined plane, smooth wood block, spring scale, meter stick Set up:
Procedure: 1. Make sure the incline plane and block are clean. 2. Set the incline so that the block just slides down. Measure the length of the incline and the height of
the incline. Record information in the data table you create. 3. Place the block at the bottom of the incline. 4. Hook the spring scale to the block and pull the block up the plane at a constant velocity. Read and
record the force measured by the spring scale. Discuss what this force on the spring scale represents and determine the force equation for this condition. It is a good idea to develop a free body diagram to help you work through this. Run at least three trials to confirm your data.
5. Place the block at the top of the incline with the spring scale attached. Let the block slide down the incline at a constant velocity. Read and record the force measured by the spring scale. Discuss what this force on the spring scale represents and determine the force equation for this condition. It is a good idea to develop a free body diagram to help you work through this. Run at least three trials to confirm your data.
Data:
Create a data table for the collection of information required to complete this lab.
Motion
mg
Spring Scale
Fspring
scale
Ff
θ
h
N
Motion
mg
Spring Scale
Fspring
scale
Ff
θ
h
N
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Analysis: Using the equations you developed in part 4. & 5. of the procedure, determine the inclined plane force component in the x-direction for each trial.
1. Calculate the work done by the mgx force (hint, direction matters). 2. Using the equations for the forces, the force of friction can be calculated. 3. Calculate the work done by the friction force (hint, direction matters). 4. Calculate the work done by the pulling force (hint, direction matters). 5. Add the work done by the pulling force and the friction force. 6. Calculate the potential energy. 7. How does the total work done by the pulling force and the friction force compare to the final/initial
potential energy for each trial? 8. How does the work done by the mgx force compare to the total work done by the pulling force and
the friction force? 9. How does the work done by the mgx force compare to the final potential energy? 10. What did you learn from this lab?
How could this lab be improved or changed to yield better results
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Two Dimensional Momentum
Purpose: To compare both head-on and non-head-on elastic collisions between objects of equal mass and unequal mass.
Method: Part I. Select two nickels of equal mass. Place one nickel as a stationary target on a
piece of paper and draw a circle around it. “Shoot” the second nickel toward the first, either by flipping it with your thumb and finger or by setting up a ramp with a piece of cardboard and letting the nickel slide down the ramp. When both nickels stop, draw the
trajectories of both nickels on the piece of paper and measure the angle between the trajectories. Do this enough times that you get at least three “head on” collisions and
three that are not head on. Part II. Repeat Part I, this time using two nickels that are not exactly of equal mass.
Data Analysis: Record all data in your book, including the masses of the nickels used in each part.
Attach to your book the paper(s) on which drawings of trajectories. Make all relevant conclusions, using averages of the measured readings. Show the mathematical derivation of velocities v1 and v2 after the non-head-on elastic
collision between two nickels of equal mass, starting with:
v1
v
m1 m2
v2
equation 1 x-direction: mv = mv1cos + mv2cos (Cons. of Momentum)
equation 2 y-direction: mv = mv1sin + mv2sin (Cons. of Momentum)
equation 3 ½ mv2 = ½ mv1
2 + ½ mv22 (Conservation of K.E…..elastic)
[note: Basically, you are proving that a right angle forms, by showing that + = 90] *Experiments similar to this are done with particles in a Supersonic Super Collider. Our experiment definitely involves only subsonic speeds.
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Torque Lab Purpose: To use torque to find the mass of an unknown.
Theory: Static equilibrium requires that the sum of the torques on a system is zero. It also requires that the sum of the forces is zero. In equation form
= 0 F = 0 In this lab, you‟ll use torque to determine the mass of an unknown. An individual torque can be
calculated using the equation = r F sin .
Equipment: 1 meter stick 1 meter stick support and support clip 3 hanger clips
2 mass hangers and set of masses unknown mass
Prelab Setup:
1. Measure and record the mass of your meter stick and all clips, and record these masses in a table of data.
2. Find the center of mass of your meter stick. Do this by balancing it on the support with the support clip. It should be near the middle, but probably will not be exactly in the middle. Record the meter stick center of mass.
3. Move the meter stick support clip 10 - 20 cm away from the center of mass of the meter stick.
4. You are now ready to ask for an unknown mass. Procedure: Devise a method to find the mass of your unknown using torque. You must leave the meter stick support clip 10 – 20 cm away from the meter stick center of mass to do this. At your disposal are your hanger clips, your mass hangers and your set of masses. After you have found the mass of your unknown, alert your instructor. He or she will check the mass of your unknown on a triple beam balance. Data: Must include all masses and meter stick positions, clearly labeled. Drawings: Must include a labeled sketch of your setup. Also must include a diagram showing all forces and moment arms, clearly labeled. Discussion: How close did you get to the actual mass using this method? What was your percent error? What did you have to include in your torque calculations? How does what you did relate to the operation of the triple beam balance you use in lab?
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Fluid Statics Lab Purpose(s): To qualitatively observe how the buoyant upward force on an object changes as an object is partially or entirely submerged in a fluid. To compare the buoyant force to the weight of the displaced fluid for a submerged object.
Theory: Archimedes principle states that the buoyant upward force on an object entirely or
partially submerged in a fluid is equal to the weight of the displaced fluid (Fb = mg = Vg, where
Fb is the buoyant force, is the fluid density, V is the volume of displaced fluid, and g is the acceleration due to gravity). The volume of the displace fluid can be determined by the volume of the submerged portion of the object. Equipment: Ruler Spring Scale Styrofoam cup or Beaker Submersible Objects Balance or Digital Scale Ring stand and support Method: 5. Measure and record the mass of a submersible object. 6. Using vernier calipers, measure and record the dimensions of your submersible object. 7. Suspend the object from the spring scale with a string. Read and record the force reading. 8. Position a Styrofoam cup or Beaker under the object. 9. Gradually add water to the cup or beaker so that the object is gradually submerged. Note
what happens to the force reading as more and more of the object is submerged. 10. When the object is completely submerged, read and record the force reading. 11. Repeat twice, for a total of three different trials with three different submersible objects.
Analysis: 1. Calculate the volume of each object from the dimensional measurements. 2. Draw two force diagrams. The first should represent the forces on the object when it is not
submerged. The second should represent the forces when the object is completely submerged.
3. Calculate the buoyant force. Use the second force diagram as the basis of your calculations. 4. From the buoyant force, the volume of displaced water, and the buoyancy equation, calculate
the density of water. 5. Compare your calculated density with the accepted value. Discussion: What happened to the force readings as more water was added to the Styrofoam cup or Beaker? At some point, did the force readings stop changing? Discuss any possible sources of error in your calculations. How might this experiment be improved?
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Fluid Dynamics Lab OVERVIEW
During the 18th
century the Swiss mathematician Bernoulli derived an important relationship regarding fluid flow. It states that the where the velocity of a fluid is high, the pressure is low, and where the velocity of the fluid is low, the pressure is high. It is this principle that explains why airplanes can fly, why large municipal water systems are possibe, and why curve balls curve in baseball. In order to develop Bernoulli‟s principle quantitatively, the work-energy theorem, W = ΔK +ΔU, and the conservation of energy are applied to fluid flow. In such a case, there are three things to be considered: kinetic energy, potential energy and work associated with a difference in pressures. For fluid flow the potential energy has two components, a pressure-related term and a gravity-related term. Putting these components into the form of energy per unit volume by using density terms, one can derive Bernoulli‟s equation:
P1+1/2 ρv1
2+ρgy1=P2+1/2ρv2
2+ρgy2
or put another way:
P+1/2ρv2+ρgy=constant
In this lab you will apply Bernoulli‟s equation in order to determine the velocity of water squirting from a hole in a plastic bottle filled with water. 1. First, you will take several measurements - the height of the water in the bottle and the
distance the water squirts from a hole in the bottle at different times. 2. Next, you will use the data and Bernoulli‟s equation to determine the velocity of the water
exiting the hole in the bottle at the different times. 3. You will then calculate the velocity of the water exiting the hole in the bottle at the different
times using the equations for projectile motion. 4. Finally, you will compare the velocities calculated by the two different methods. LAB EQUIPMENT AND MATERIALS Meter Stick, Plastic Soda Bottle (2 liter), nail, Sharpie Marker, Water LAB PROCEDURE Hints for a successful lab: Do this experiment in an area where it is okay that the floor gets wet. Do not try to measure water heights and distances during the experiment, just make marks and take measurements later. Prepare the bottle and lab area 1. Fill the plastic bottle with water.
2. Place the bottle near the edge of a small table or stand in an area where the floor may get wet.
Perform the water flow procedure
1. Poke a small hole near the bottom of the bottle with the nail.
2. Cover the hole with your finger to stop the water flow.
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3. Mark the initial height of the water level on the bottle.
4. Mark the height of the water on the bottle and the corresponding distance the water is squirting
on the floor.
5. Repeat the marking of height and distance five or six times before the bottle empties.
Perform measurements and record data
1. Measure the height of the hole above the floor and record on the data sheet.
2. Measure the depth of the hole below the water surface for each mark and record on the data
sheet.
3. Measure the distance the water squirted for each mark on the floor and record on the data
sheet.
4. Measure the height of the hole above the floor and record on the data sheet.
5. Calculate the height of the water surface above the floor and record on the data sheet.
Cleanup lab
1. Mop/clean up water mess on the floor.
2. Properly dispose of (recycle) the plastic bottle, nail and any other trash that was generated.
3. Put away meter stick.
LAB REPORT/ANALYSIS QUESTIONS
Provide answers to the following questions using complete sentences.
1. What is the pressure of the water at the surface and the pressure of the water upon leaving the
bottle?
2. Estimate the velocity of the water near the surface and discuss how it compares (qualitatively)
to the velocity of the water exiting the bottle.
3. Derive an expression for the velocity of the water exiting the bottle based on Bernoulli‟s
equation. Calculate the velocity for each of the water depth marks in your experiment and record
on the data sheet.
4. Derive an expression for the velocity of the water exiting the bottle based on the equations for
projectile motion. Calculate the velocity for each of the water depth marks in your experiment and
record on the data sheet.
5. How do the water velocities calculated from Bernoulli‟s equation and the equations for
projectile motion compare to each other? Explain any differences.
6. Draw a Schematic diagram of experimental apparatus.
7. Create a Data Table for the collection of lab information.
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Thermodynamics Lab Purpose: To calculate the efficiency of an automobile engine
Pre-lab: What do you consider a “good efficiency” for an automobile engine?
What are some factors that affect engine efficiency?
Discussion: Efficiency is defined as the ratio of the actual work done to the amount of heat absorbed.
EfficiencyW
Qh
W = Work done by the engine to overcome drag Qh= heat produced by burning gas
Part I – Calculating the WORK 1. Find a level stretch of road with little traffic. 2. Obtain a speed of 55 mph.
3. Measure and record the amount of time it takes to COAST to 45 mph. 4. Repeat steps 2 & 3 five times to get an average.
Time 1 Time 2 Time 3 Time 4 Time 5 Average Time
Part II – Calculated the Heat Absorbed by the engine 1. Measure and record your weight in kilograms 2. Measure and record the weight of any passengers.
3. Measure and record the weight of the car. This can be found on a sticker that is usually on the inside door jam on the drivers side.
4. Fill up gas tank completely with gas. 5. Set odometer to “00” 6. Find a level stretch of road that will accommodate cruise control.
7. Set cruise control at 50 mph and drive 40 miles. 8. At the end of the trip, refill your gas tank. 9. Measure and record the amount of gas used for the trip
10. Measure and record the final odometer reading. Mass of occupants in kilograms _________________ Mass of car in kilograms_______________
Total distance traveled in meters ________________ Total amount of gasoline used in Liters ______________
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Part I – Calculations
Since av
t
, solve for the deceleration of the car.
Since we are moving at a constant speed in Part II, the force supplied by the
engine must be equal to the drag force or friction. Using Newton’s second law, calculate the drag force.
Since we are moving at a constant speed the engine must to WORK against
the DRAG force. Find the WORK done by the engine. The displacement in this case is the total odometer reading converted to meters.
Part II – Calculations Using the known value for the density of gasoline (0.74 kg/L), calculate the
mass of gasoline used.
As the gas ignites it turns into a gas. The heat given off is directly proportional to the mass. When a substance CHANGES STATE we call this latent heat. The formula for latent heat of vaporization is:
Q mLh Where; m = mass of gasoline used and
L = latent heat constant for gasoline= 4.6 x 107 J/kg
Solve for HEAT ABSORBED
Calculate the efficiency of the engine
What do you consider a “good efficiency” for an automobile engine NOW?
What are some factors that affect engine efficiency?
Explain what happened to the Heat that was not used by the engine to do useful work.
