Stress, strain and the Young modulus

Question 1

what is one big disadvantage of using the spring constant as a description of material behaviour?

Answer 1

the spring constant will vary from sample to sample of a material, depending on the dimensions

Question 2

what’s the equation that connects cross sectional area, length and spring constant?

Answer 2

k=A/L

Question 3

give a definition of the term stress, include its units

Answer 3

force per unit area
F in N
A in m^2
units: Pa or Nm^-2

Question 4

what’s the equation of stress?

Answer 4

stress (sigma) = F/A

Question 5

give a definition of the term strain, give the units

Answer 5

extension (or compression) per unit length
no units! (it’s a ratio)

Question 6

give an equation for strain

Answer 6

strain (epsilon) = x/L

Question 7

give a definition of the term Young’s modulus and its units

Answer 7

E = the ratio of stress to strain for a material
units: Pa or Nm^-2

Question 8

what are the 2 equations for Young’s modulus?

Answer 8

E=stress/strain
E=FL/Ax

Question 9

what measurements need to be taken to find the Young modulus of a sample of wire and which equipment needs to be used?

Answer 9

• diameter of wire, using a micrometer
• length (& extension) of wire, using a meter rule?ruler
• weight of masses, using a balance

Question 10

describe the procedure for finding the Young modulus of a sample of wire

Answer 10

1. set up the wire in the frame, ensuring it’s straight and properly secured at both ends
2. measure diameter of wire with a micrometer at multiple points and find the average & the initial length of the wire
3. gradually add weights and measure the extension at each step
4. calculate stress (F/A)
5. calculate strain (x/L)
6. plot stress-strain graph (the slope of the linear region = the Young’s modulus)

Question 11

describe any potential sources of uncertainty and how you can mitigate against them when finding the Young modulus of a sample of wire

Answer 11

• length/extension - use precise measuring tool, ensure measurements are taken from a fixed point and take the average
• CSA measurements - measure at multiple points and calculate the average
• weight - correctly calibrated digital scale
• temperature - conduct experiment in controlled environment with a stable temperature
• elastic limit - if exceeded, deformed wire gives inaccurate measurement

Question 12

describe how the force constant of a compression spring can be verified in the laboratory

Answer 12

1. add mass to spring and find F=mg for each mass
2. record compression for each mass
3. plot graph of F vs compression
4. gradient = spring constant