Properties of Materials

Question 1

What is weight and how can it be calculated?

Answer 1

• Weight is the pull of gravity on an object

- W=mg

Question 2

What is work done? How can it be calculated?

Answer 2

• Work done (or energy transferred) by a force on an object depends on the magnitude of the force in the direction of motion of the object
• W=F(magnitude of force) x s (distance moved in the direction of the force) costheta (angle between the force and direction in which the object moves)

Question 3

What is density?

Answer 3

• Density is a measure of the mass per unit volume

- Density=mass/volume

Question 4

What are compressive forces?

Answer 4

• Compressive forces are forces that tend to squeeze an object and reduce its size in the reaction that the forces are applied
• For example, a heavy weight placed on a column, together with the upwards force on the bottom of the column will reduce the height of the column

Question 5

What are tensile forces?

Answer 5

• Tensile forces are forces that act to pull or stretch an object
• The metal ropes holding up a lift have tensile force acting on them due to the weight of the lift and the upwards pull from the ceiling on the end of the rope

Question 6

What is Hooke’s law?

Answer 6

1. The extension is proportional to the force applied

2. F=Kx

Question 7

What is the spring constant, k?

Answer 7

• It is a measure of how hard it is to bend or stretch a spring
• A large spring constant means that the spring is stiff
• Units: Nm-1

Question 8

What is the extension, x?

Answer 8

• It is the length a material has stretched when a load is added
• It is calculated by subtracting the original length of the material from the length when stretched

Question 9

What is the limit of proportionality?

Answer 9

It is the endpoint of the linear section of a force-extension graph

Question 10

What is the elastic limit? What determines if a material is elastic?

Answer 10

1. Elastic limit is the load above which a material is permanently deformed
2. A material is said to be elastic when it returns to its original dimensions once the applied load is removed
3. A material is said to be plastic when it is permanently deformed and does not return to its original dimensions once the applied load is removed

Question 11

Why does a wire obey Hooke’s law?

Answer 11

1. Wires obey Hooke’s law because the bonds between the metal atoms act like spring and so when the wire is stretched the bonds lengthen slightly and when the force is removed, the bonds return to their original length
2. However, if the force applied is too great and the elastic limit is exceeded then the metal atoms will be able to move past one another and the wire lengthen, this is known as ductility and is a very useful property as it allows metals to be formed into thin wires
3. The wire formed shows plastic behaviours and will not return to its original length when the force is removed. Ductile behaviour is also an example of plastic deformation
   - Ductile materials can be formed into wires y stretching them. They show ductility

Question 12

What does brittle mean?

Answer 12

1. Some materials do not show plastic behaviour but are brittle and break when the elastic limit is exceeded. Cast iron and glass are two examples of brittle materials
2. The way in which ductile and brittle materials fracture is also different, in a ductile material, the sample of material will elongate and ‘neck’ before it breaks
3. On a force-extension graph, necking occurs in the plastic region of the graph and in a bridle material there is no. change int he shape of the material because it does not undergo plastic behaviour; a straight break in the material is seen
   - A brittle material is one that shows little, or no plastic deformation before breaking

Question 13

What is elastic strain energy?

Answer 13

• The energy stored by stretched materials

- The elastic strain energy stored is equivalent to the work done in stretching the material

Question 14

What happens when a material is stretched or compressed?

Answer 14

1. Its elastic strain energy is altered
2. The elastic properties of some material, such as rubber can be complex as when a rubber band is stretched it will return to its original length however the way in which it does this is very different from a metal wire

Question 15

Describe the loading and unloading curve of a rubber band

Answer 15

1. Initially there is a small amount of extortion as the force is applied
2. Then as more force is applied, the rubber band stretches easily
3. Finally, just before it breaks it becomes harder to stretch again
4. The extension for a given force is different when the rubber band is being loaded or unloaded
5. This means that the strain energy stored when the rubber band is being loaded is greater than the strain energy related when the rubber band is being unloaded
6. However the law of energy conservation states that energy cannot be created or destroyed in a closed system
7. Therefore the difference in strain energy must be accounted for; in the case of the rubber band, it will come warm s it is stretched and relaxed and this is why there is a difference in energy between loading and unloading

Question 16

What is tensile stress?

Answer 16

1. Tensile stress is the measurement of the force applied over the cross section area of a sample of material
2. Stress = Force / Area

Question 17

What is tensile strain?

Answer 17

1. Tensile strain is the ratio of the extension and the original length of the sample
2. Strain = extension / original length

Question 18

What is the Young Modulus, E?

Answer 18

1. Is a measure of the stiffness of an elastic material, It does not depend on the dimensions of the sample being tested. It is measured in Pa or Nm-2
2. E = Fl / AdeltaL

Question 19

How do you interpret stress strain graphs?

Answer 19

1. Stress-Strain graphs allow us to describe the properties of material, and also to predict the stresses at which changes in those properties might occur
2. Ceramics: extremely strong and have very high UTS values and show very little (if any) plastic behaviour before they fracture so they are also very brittle
3. Glasses: have lower UTS values than ceramics and so are less strong but they are also brittle,generally showing no plastic behaviour before they break
4. Copper: has a long plastic region because it is a ductile material and this makes it ideal for forming into wires for use in electrical circuits

Question 20

Describe steel

Answer 20

1. Steel is same by adding different elements t upon to form an alloy
2. Common elements used in steel-making are carbon, manganese and chromium and types of steel differ in the percentage composition of the various elements added to iron to create them
3. This affects the properties of steel and they are generally much stiffer than ductile metals such as copper giving. lower value of Young modulus

Question 21

Describe high-carbon steel

Answer 21

1. It is strong but brittle material
2. It shows elastic behaviour at higher values of stress but fractures with very little plastic behaviour
3. This type of steel is often sued in cutting tools and drill bits because it has a higher UTS value
4. Other types of steel may show plastic behaviour but have a lower UTS value

Question 22

What is strain energy density?

Answer 22

• The strain energy density is the strain energy per unit volume of a sample
• You can calculate the strain energy density which is a measure of the energy stored in a material that does not depend not the dimension of the sample being tested
• 1/2 x (stress x strain)
• It is the area under a linear, stress-strain graph and therefore the area under any stress-strain graph is equal to energy per unit volume

Question 23

How do you find the young modulus of a wire?

Answer 23

1. The test wire should be thin, and as long as possible. The longer and thinner the wire, the more it extends for the same force-this reduces the uncertainty in you measurements
2. First, you need to find the cross-sectional area of the wire. Use a micrometer to ensure the diameter of the wire in several places and take an average of your measurements. By assuming that the cross section is circular, you can use the formula for the area of a circle being pir^2
3. Clamp the wire to the bench (as shown in the diagram above) so you can hang weights off one end of it. Start with the smallest weight necessary to straighten the wire (don’t include this weight in you final calculations).
4. Measure the distance between the fixed end of the wire and the marker, this is your unstretched length
5. Then if you increase the weigh, the wire stretches and the marker moves
6. Increase the weight in steps (e.g. 100g intervals), recording the marker reading each time - the extension is the difference between the reading and the unstretched length
   - To avoid random error you should use a thin marker on the wire and always look directly at the marker and ruler when measuring the extension
7. You can use your results from this experience to calculate the stress and strain of the wire and plot a stress-strain curve
   - The other standard way of measuring the Young Modulus in the lab is using Searle’s apparatus. This is a bit more accurate, but it is harder to do and the equipments more complicated

Question 24

Describe how the length and extension of the wire could be measured experimentally and explain what safety precautions should be taller when carrying out measurements

Answer 24

1. Original length measured with a ruler
2. Extension may be measured a vernier scale fixed to a reference wire hung next to the sample wire
3. Safety goggles must be worn when measuring extension in cases of wire breaking
4. Cushioning placed under the weights to prevent damage to floor or feet incase of wire breaking

Question 25

What is the effect of not taking repeat measurements?

Answer 25

Increase the likelihood of incorrect readings as random errors will be less obvious

Question 26

Using a graph does and elastic band show Hooke’s law behaviour?

Answer 26

• No
  1. Hooke’s law states that the force is proportional tot the extension and will give a straight line graph
  2. The elastic band does not have a straight line force-extension graph so does not show Hooke’s law behaviour

Question 27

Describe a simple experiment that would allow measurement of the force applied and the extension of the elastic band

Answer 27

1. Elastic band suspended from a fixed point
2. Fix a ruler close, parallel, to the band
3. Unstretched length measured. Ensure that the band is straight to reduce measurement error (small pointer attached to bottom of band could be used to aid reading)
4. 100g mass hanger added and new length measured
5. Masses continue to be added in regular increments and length measured each time
6. To measure unloading, the masses are removed, again in regular increments, and the length measured once each mass has been removed