Edexcel AS Physics for Assessment in 2016 Paper 2: Core ...sophysics.co.uk/images/teaching/Topic_4_STUDENT_NOTES.pdf · Topic 4 - Materials 1 2016 Edexcel AS Physics for Assessment

Topic 4 - Materials 1 2016

Edexcel AS Physics for Assessment in 2016

Paper 2: Core Physics II

Topic 4: Materials

In this topic we’ll be studying some of the properties of fluids and the effects of applying stretching and compressing forces to solid objects. We’ll be carrying out experiments to see what happens when we apply a stretching force to a wire or a spring and drawing graphs to interpret our results. Key terms to understand in topic 4 are stress, strain, Young’s modulus of elasticity, elastic and plastic deformation and elastic limit. You will also need to recall ideas from the mechanics topic as we will be finding the terminal speed of a mass falling through a fluid and using this to calculate the viscosity. In addition to the exercises in these notes, you will complete additional work from the text book and several assessed homework sheets. To complete this topic you will need the following mathematical skills:

Understanding what is meant by the term inversely proportional and knowing how to test for an inversely proportional relationship between two variables

Understanding the equation of a straight line graph and calculating gradients

Converting between different area and volume units (e.g. cm2 to m2 or mm3 to m3) If you are not confident with these skills then you should attend the physics workshop for extra practice.


Section 1 – Density

This section covers point 49 in the exam specification

1.1 Mass and weight (49)

As you will recall from your studies in school the mass of an object is not the same thing as its weight. Mass – Weight – If we know the mass of an object we can calculate its weight on the surface of the earth using the following formula

1.2 Density Look at the grid below and work out how many dots there are in every big square. ANSWER = ________________ dots per big square ________________ dots per little square That was an easy example because there was the same number of dots in each big square. We could say that the squares were uniformly distributed across the squares. Let’s try a more difficult example. ANSWER = ________________ dots per square

Weight = mass x


The density of an object tells us how much mass there is in a given volume. The symbol for density is the Greek letter rho ( ρ)

Definition The density of an object is its mass per unit volume

(Density) Units of Density: Worked Example The mass of the Earth is 5.97 x 1024 kg. The radius of the Earth is 6.37 x 106 m. Calculate the density of the Earth.

Density Questions

1. A block of iron of volume 0.5m3 is found weigh 39500 N. Calculate the density of iron.

2. The radius of the Sun is 6.96x108m and has an average density of 1410 kgm-3. Calculate the

mass of the Sun. 3. The volume of a uranium nucleus is 1.7x10-42m3 and its mass is 3.95x10-25kg. Calculate the

density of the nucleus. 4. A room is 3.5m wide, 4.2m long and has a height of 2.4m. Given that the density of air at

room temperature is 1.21kgm-3 what is the weight of the air in the room?

v

m


1.3 Measurement We have seen that if we want to find the density of an object we need to know the object’s mass

and volume. In the previous questions these values were provided, but in the real world we would

need to measure them.

Vernier Callipers

Vernier callipers can typically be used to measure lengths

accurate to the nearest 0.1 mm. This is achieved by looking at

the alignment of the moving Vernier scale with the fixed scale.

The object to be measured is placed between the callipers.

The fixed scale gives the length in mm. In this example the length is exactly 5.0 mm

For lengths slightly beyond 5.0 mm we look for the Vernier mark that is exactly aligned with a fixed scale mark.


The Micrometer A standard micrometer will measure to the nearest 0.01 mm. The graduations along the length of the

barrel of the micrometer are in mm and the scale around the thimble (the part that turns) is in 0.01

mm. Before we use the micrometer

we must close the jaws and check for

zero error. This means that when the

micrometer is closed the scale should

read zero. If it does not, then we must

adjust all of our measurements to take

account of the zero error.

This micrometer reads 7.00 mm. Can you

find the readings on the others?

Science Vocabulary

If there is any zero error then all of the measurements

taken will be different from the true value by the same

amount. This is what is known as a systematic error as

it is the same for all measurements. Reducing the

systematic error will improve the accuracy of the

measurement.

Use the ratchet to close

the micrometer so that you

do not over tighten the

screw. This scale on the barrel

has marks that represent

every half mm opening of

the micrometer.

This scale on the thimble

has marks that show every

0.01 mm.

You can lock a measurement

into the micrometer with this

lever. This should make it

easier to take readings.


Reducing the random error in measurements

We can reduce the random error by

making several repeat readings and

then taking an average. For example,

the thickness of a metal plate might

vary randomly as we move across the

surface. Taking repeat readings at

several different places across the plate

and then finding an average thickness

would smooth out the random variations

and give us a better value for the

thickness.

Science Vocabulary

Random error will cause each measurement to be

different from the true value by a different amount.

Having lots of random error will reduce the precision of

our measurements. We can reduce the random error by

taking multiple measurements (at different places when

necessary) and finding the average value.


1.4 Finding the density of some regularly shaped objects

You will have been provided with a selection of materials. Take measurements from the materials and complete the table. Remember to take repeated measurements of the objects’ dimensions at different places so that random error is reduced.

Material l1 / mm l2 / mm l3 / mm V / mm3 m / g ρ / g mm-3

Brass

Lead

Aluminium

Wood

Paraffin Wax

Steel

Polystyrene

Copper

Notice how the column

headings are set out…

Quantity / Unit

Don’t forget about getting the SIGNIFICANT FIGURES correct.

If you are measuring with a ruler then you should record

the values to the nearest mm. The Vernier callipers will

give you values to the nearest 0.1 mm (or 0.01 if digital

callipers are used) and the micrometer will go to 0.01 mm.


Further Density Questions

These questions get more difficult as you work down the page. The first 6 questions are compulsory and the remainder are extension tasks.

1. Calculate the density of a rectangular block 2 m by 1 m by 7 m if its mass is 24 000 kg.

2. Calculate the density of the plastic foam used to make a sheet 2.0 m by 1.0 m by 100 mm if its

mass is 4.0 kg.

3. A large concrete block of volume 0.5 m3 has a mass of 1300 kg. What is the density?

4. A small block of aluminium has a volume of 6.00 × 10-6 m3 and a mass of 1.62 × 10-2 kg. What is its density?

5. A laboratory is 15 m long, 8 m wide and 4 m high. What mass of air does it contain?

6. A cylindrical metal rod of density 7 000 kg m-3 and diameter 40.0 mm has a mass of 1.76 kg.

What is the length of the rod?

7. A tangle of wire of density 8 400 kg m-3 and diameter 2.00 mm has a mass of 1.056 kg. Calculate the length of wire which has been tangled.

8. A container holds 2.4 kg of brine. This is used up and is replaced by 4.0 kg of sand of density 3 200 kg m-3. The container is then filled up with water. What mass of water is needed?

9. A bottle contained 200 g of a liquid of density 800 kg m-3. The liquid is emptied out and 160 g of sand is put in. What mass of water can now be poured in to fill the bottle?

10. A porous metal cube of side 100 mm is made from metal of density 8 000 kg m -3 and has a

mass of 7.2 kg. Calculate the volume of the pores in the metal if the mass of air that they contain can be neglected.

11. A rectangular metal block of dimensions 200 mm by 100 mm by 100 mm has a hole in the middle. If the metal has a density of 6 000 kg m-3 and the block has a mass of 9.0 kg, calculate the volume of the hole.

12. 0.000 300 m3 of water is mixed with 0.000 200m3 of a liquid of density 1500 kg m-3. If there is no change in the volume of the two liquids upon mixing, what is the density of the mixture?

13. 0.000 500 m3 of a liquid of density 800 kg m-3 are mixed with 0.000 300 m3 of a liquid of density 1200 kg m-3. What is the density of the mixture if there is no change in the volumes of the liquids on mixing?

14. A liquid mixture of water and alcohol has a density of 850 kg m-3. What is the proportion of each liquid (a) by volume, (b) by mass in the mixture?

15. An alloy has a density of 8000 kg m-3. It is made from two metals of densities 10 000 kg m-3 and 7200 kg m-3. What is the proportion of each metal (by mass) in the alloy?

Useful Density Data

Air 1.23 kg m-3

Alcohol 800 kg m-3

Paraffin 800 kg m-3

Water 1000 kg m-3

Brine 1200 kg m-3

Sea Water 1250 kg m-3

Mercury 13 600 kg m-3


Exam question


Section 2 – Viscosity, upthrust and drag This section covers points 50 and 51 in the exam specification 2.1 Archimedes’ principle (50) Archimedes principle states that when you immerse a body in some fluid the upthrust is equal to the weight of the fluid that is displaced. We can use this idea to solve lots of problems. Problem 1 A plastic buoy is to be anchored to the bottom of the ocean. The buoy is a hollow, rigid plastic sphere that is incompressible. The weight of the plastic is 1.0 kg and the radius of the buoy is 0.20 m. The buoy contains air of density 1.2 kg m-3. The density of seawater is 1250 kg m-3. The buoy is anchored to the sea bed by means of a rope that prevents the buoy from floating to the surface. What is the tension force on the rope? Step 1 – Calculate the volume of air in the sphere Step 2 – Calculate the weight of the air in the sphere Step 3 – Calculate the total weight of the buoy (yes, air has weight!) Step 4 – Calculate the volume of the seawater that is displaced by the buoy Step 5 – Calculate the mass of the seawater that is displaced by the buoy Step 6 – Calculate the tension needed on the rope to keep the buoy in equilibrium


Problem 2 A helium filled balloon is attached to a string. The weight of the elastic that makes up the balloon is 0.01 kg and the balloon is a sphere of radius of 0.10 m. The density of air is 1.2 kg m-3 and the density of helium is 0.16 kg m-3. Calculate the tension in the string that is preventing the balloon from accelerating up into the air. Problem 3 The string attached to the balloon in problem 2 is cut. What is the initial acceleration of the balloon?

Problem 4 A hot air balloon contains 2800 m3 of hot air of density 0.95 kg m-3. The density of air outside the balloon is 1.20 kg m-3. If the balloon is floating at a constant height above the ground, what is the total weight of the balloon and everything attached to it?

Problem 5 A ballast weight of mass 20 kg is dropped from the balloon. What is the initial acceleration of the balloon? Problem 6 A cylindrical fishing float of radius 0.5 cm and length 10 cm is attached to a lead weight with a mass of 5 grams. The density of the fishing float is 5 g cm-3. The float and the weight are cast into a freshwater lake (water density 1000 kg m-3). The float comes to equilibrium with the upthrust equal to the weight. What length of the float is above the surface of the water? (TAKE CARE WITH THE UNITS!)


Examination Question

The picture shows a submarine and one of the forces acting on it as it moves along at a constant depth and speed in the direction shown.

a) Add labelled arrows to show the other three forces acting on the submarine.

b) State two equations that show the relationship between the forces acting on the submarine.

c) The submarine has a volume of 7100 m3. The density of seawater is 1030 kg m-3. Show that the weight of the submarine is about 7 x 107 N.


Section 2.2 – Viscous drag (51) If a body is moving through some fluid, then the fluid will exert a drag force on the body. If you try

running through deep water or dragging a spoon through some honey, then you can experience this

for yourself. The drag force is caused because work must be done to move the fluid out of the way.

The harder the fluid is to push out of the way, the larger the drag force. If a fluid flows easily (e.g. air)

then it will be easy to push out of the way. If a fluid does not flow easily (e.g. syrup) then a much larger

drag force will be produced. The technical name for ‘how easily a fluid flows’ is the viscosity.

We are only going to worry about spheres moving slowly through a fluid. If the speed gets large, or we

have some other shape then things get more difficult. The drag force on a slowly moving sphere is

given by Stokes’ Law. This will be on the formulae sheet in your exam.

F = 6 π η r v

You should write down what each of these terms stands for and work out the units of viscosity.

Problem 1

A metal sphere of mass 0.01 kg and diameter 2 cm is dropped into some honey. The viscosity of the

honey is 5 N m-2 s. The sphere quickly reaches its terminal speed with the weight force becoming

equal to the drag. What is the terminal speed of the sphere?

Problem 2

A spherical bubble of air in some oil has a volume of 5.24 x 10-10 m3. The density of the air is 1.21 kg

m-3 and the density of the oil is 880 kg m-3. The viscosity of water is 0.32 N m-2 s. The bubble is

moving upwards at a constant speed. Find the speed of the bubble.

Step 1 – Calculate the weight of the air in the bubble.

Step 2 – Calculate the weight of the oil that is displaced by the bubble.

Step 3 – Calculate the drag force that must act on the bubble so that the resultant force is zero.

Step 4 – Use Stokes’ Law to calculate the speed of the bubble


Section 3 – Elastic behaviour This section covers points 53, 54, 55 and 58 in the exam specification 2.1 Stretching springs We are going to look at what happens when a stretching force is applied to a spring. Use the

equipment provided to add masses to the end of a steel spring. Record your measurements in a table

in the space below then draw a graph showing how the stretching force (tension) causes the extension

of the spring to change.

.

Laminar and Turbulent Flow


How your physics examiner will mark your graph

Section 2.2 – Hooke’s Law (53) The graphs on the previous page show clearly that there is a simple relationship between the

extension of the spring and the stretching force. You may have seen straight line graphs like this

before – they indicate a directly proportional relationship between the two quantities. The discovery

of the directly proportional nature of the relationship between tension and extension was discovered

by Robert Hooke in the 17th century.

You must make sure

that your data points

cover at least ½ of the

page vertically and ½

of the page

horizontally

You must

make sure that

you label your

axis correctly.

Make sure that you use sensible scales. Your

y-axis doesn’t have to start at zero.

Plot your points with a

sharp pencil using ‘+’

symbols.

Science Vocabulary

Directly proportional means that if we draw a graph

showing how two quantities are related then that graph

will be a straight line that passes through the origin of

the graph. These sorts of graphs will be described by an

equation like y = a x , where a is the gradient of the

graph.


If we combine two or more springs together in series, the behaviour of the system will change. By

linking springs together end on end and repeating the experiment, we can find out how the stiffness of

the system changes with the number of springs that are chained together. If n is the number of

springs, theory suggests that the stiffness of the system will be inversely proportional to n. Written

as an equation, this means that…

If we plot a graph with 1/n on the horizontal axis and the stiffness of the system on the vertical axis

then we should get a straight line. Find the stiffness of systems of two, three and four series springs

and then draw a graph to test if the theory is correct.

Section 2.3 – Energy stored in a stretched spring (58)

We can use a force extension graph to help us work out the energy stored in a spring under tension.

First we need to recall the equation for the work done by a force.

From the equation above we can see that work done has units of ______________________

Now we can take another look at the force extension graph. We have already interpreted the gradient

of the graph – now we will look at the area under the graph.

NOT EVERY STRAIGHT LINE

REPRESENTS A DIRECTLY

PROPORTIONAL RELATIONSHIP. IF

THE LINE DOESN’T GO THROUGH

THE ORIGIN THEN IT’S NOT

DIRECTLY PROPORTIONAL


Springs in Series and in Parallel


Section 2.4 – Hooke’s Law Problems (Answer on A4 lined paper)

1. A 5 kg mass is suspended from a spring. The spring extends by 2 cm. What is the value of k

for the spring?

2. What force is required to cause an extension of 75 mm in a spring of stiffness 20 Nm-1?

3. A mass of 8 kg is supported by four parallel springs of stiffness 120 Nm -1. Find the tension on

each spring and the extension of each spring.

4. Two identical springs are set up in parallel to support the weight of a 12 kg mass. The weight

of the mass causes the springs to extend by 13 cm. What is the spring constant for the

system of springs?

5. A third spring is added to the system described in question 4. If the third spring is identical to

the other two, what is the extension of the system now?

6. Three springs of stiffness k1, k2 and k3 are arranged in parallel. What is the stiffness of the

entire system?

7. A mass of 7 kg is supported by three springs, each of stiffness 200 Nm-1. The springs are

arranged in series. What is the tension on each spring? What is the extension of the entire

system?

8. A spring of stiffness 12Nm-1 is combined in series with a spring of 8Nm-1. What is the stiffness

of the combined system of springs?

9. You have five springs, each of stiffness k. Draw diagrams to show all of the different ways in

which these springs can be combined and calculate the stiffness for each of the different

combined systems.

10. What is the work done stretching the spring in question 1? What force is doing this work?


Section 2.5 – Stress and strain (54)

Up to now we have measured the force applied to a body and the extension produced by that force

but if we want to compare the elastic behaviour of two material samples fairly we must take account of

their different shapes.

Stress

LEARN THIS FOR THE EXAM


The symbol for stress is the lower case Greek latter ‘sigma’ (σ) Using the definition above, write down a formula for stress along with its units

Definition The tensile stress on an object is the stretching force per unit cross

sectional area


Strain Finding the stress allows us to compare objects of different cross sectional area. Finding the strain

allows us to compare objects of different lengths



The symbol for strain is the lower case Greek letter epsilon (ε) Using the definition above, write down a formula for strain along with the units

Definition The tensile strain on an object is the extension produced per unit

original length


Section 2.6 – Graphs of stress vs. strain (54)

We can draw graphs of stress and strain just like graphs of force and extension. They will have the

same shapes but the gradient and the area under the graph will have different meanings.


Section 2.7 – Hysteresis Curves

Sometimes the work done on a material when it is loaded (stretched) is not the same as the work that

the material does when it is unloaded. This effect is most obvious with materials such as rubber.

Investigation

Using 50g masses and an elastic band, collect data and draw a graph showing how

the extension of the elastic changes as a load is added and then removed from the

material.


Questions on elastic behaviour – answers to be written on a separate sheet of A4 paper

1. Consider a cylinder with cross-sectional area 0.010m2 and length 50cm. It extends 1.0cm when a force of 50N is applied. Calculate the tensile stress and tensile strain.

2. A strip of rubber originally 75 mm long is stretched until it is 100 mm long. What is the tensile

strain? Why has the answer no units? 3. The greatest tensile stress which steel of a particular sort can withstand without breaking is

about 109 Nm-2. A wire of cross-sectional area 0.01 mm2 is made of this steel. What is the greatest force that it can withstand?

4. Find the minimum diameter of an alloy cable, tensile strength 75 MPa, needed to support a

load of 15 kN.

5. Calculate the tensile stress in a suspension bridge supporting cable, of diameter of 50 mm that pulls up on the roadway with a force of 4 kN.

6. Calculate the tensile stress in a nylon fishing line of diameter 0.36 mm which a fish is pulling

with a force of 20 N.

7. The marble column in a temple has dimensions 140 mm by 180 mm.

a. What is its cross-sectional area in mm2? b. Now change each of the initial dimensions to metres – what is the cross-sectional area

in m2? c. If the temple column supports a load of 10 kN, what is the compressive stress, in N m–2? d. The column is 5.0 m tall, and is compressed by 0.1 mm. What is the compressive strain

when this happens? e. Use your answers to the questions above to calculate the Young modulus for marble.

8. A 3.0 m length of copper wire of diameter 0.4 mm is suspended from the ceiling. When a 0.5

kg mass is suspended from the bottom of the wire it extends by 0.9 mm.

a. Calculate the strain of the wire. b. Calculate the stress in the wire. c. Calculate the value of the Young modulus for copper.

9. A large crane has a steel lifting cable of diameter 36 mm. The steel used has a Young

modulus of 200 GPa. When the crane is used to lift 20 kN, the unstretched cable length is 25.0 m. Calculate the extension of the cable.

10. A steel wire 5.0m long and with a cross-sectional area of 0.01cm2 extends by 2.5mm when a

mass of 10kg is hung from one end. Calculate the value for the Young modulus for steel. (Take g = 10ms-2 to keep things simple in this case).

11. Calculate the work done if a steel wire 2.0m long and 0.010cm2 in cross-sectional area

extends by 2.5mm when a load is hung from its end. (Esteel = 200GPa)

12. A long strip of rubber whose cross section measures 12 mm by 0.25 mm is pulled with a force of 3.0 N. What is the tensile stress in the rubber?

13. Another strip of rubber originally 90 mm long is stretched until it is 120 mm long. What is the

tensile strain?


Section 3 – Plastic behaviour

This section covers points 55, 56 and 57 in the exam specification

Section 3.1 – Beyond the elastic limit (55, 56)

In your investigation of springs you probably noticed that unless you applied a large load to the

springs, they always returned to their original length when the stretching force was removed. This is

known as elastic deformation. If we apply a large enough force we can cause it to permanently

change its shape. This is known as plastic deformation.

In an experiment to find out about what happens to a sample of metal under stress, the following

results were obtained.

Strain

/10-3 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Stress

/108 Pa 0.00 0.90 2.15 3.15 3.35 3.20 3.30 3.50 3.60 3.60 3.50

Use the table to plot a graph with strain on the horizontal axis and stress on the vertical axis.


Section 3.2 – Measuring the Young Modulus (57)

If we wanted to find out the Young Modulus of a material then we would need to produce a graph of

stress vs. strain. In the space below, make a list of all of the measurements of the wire that you would

need to make before you started the experiment.

Next, we would need to carry out the experiment. Write a brief description of what you would do and

the measurements that you would record.

Finally we must say how we could use our results to find the Young Modulus.

Measurements of the wire What could be done to reduce uncertainty in

the micrometer readings?

Procedure and recording data

1.

2.

3.

4.

Calculating the Young Modulus


Finding the Young Modulus of a Wire – Examination Question

A student wishes to measure the Young Modulus of a metal in the form of a long, thin wire.

Describe a procedure that the student could follow to obtain this value.

Remember! If you’re asked to

describe something like this in

the exam then your answer

must say something about

drawing a graph.


Section 3.3 Ductile and brittle materials


Documents

Edexcel AS Physics for Assessment in 2016 Paper 2: Core ...sophysics.co.uk/images/teaching/Topic_4_STUDENT_NOTES.pdf · Topic 4 - Materials 1 2016 Edexcel AS Physics for Assessment