KCL Section 2: Stress, strain and the Young modulus (Materials)

Question 1

What is stress?

Answer 1

Stress is a measure of the force acting within a material.

Question 2

What is the difference between tensile stress and compressive stress?

Answer 2

Tensile stress causes stretching, compressive stress causes squashing.

Question 3

What are the units for stress?

Answer 3

Pa

Question 4

A thin wire has a cross-sectional area of 4 x10^-8 m and is stretched by a force of 200 N. What is the tensile stress in the wire?

Answer 4

5 x 10^9

Question 5

Nylon has an ultimate tensile stress of 7 x10^7 Pa. The cross-sectional area of the nylon rope in the diagram is 3 x 1000 m^2. Phiz weighs 600 N. Will it hold him?

Answer 5

YES

Question 6

What is strain?

Answer 6

Strain is the extension of the material compared to its original length.

Question 7

What are the units for strain?

Answer 7

There are no units because it is a ratio, you can also give it as a percentage.

Question 8

A steel wire of length 2.3 metres is stretched by 1.5 millimetres. What is the tensile strain?

Answer 8

6.5 x 10^-3

Question 9

A copper wire of length 1.76m is stretched by a force to a length of 1.80 m. What is the tensile strain in the wire?

Answer 9

2.3%

Question 10

What is Young Modulus?

Answer 10

When a material deforms elastically the stress is proportional to the strain (like force and extension in Hooke’s law). The Young modulus is a constant of proportionality that shows the stiffness of the material.
It is calculated from stress and strain, so it is a property of the material: different shaped objects made from the same material will have the same Young modulus.

Question 11

A steel wire of length 2.00m and diameter 0.40mm is extended by 4.0mm when a stretching force of 50N is applied. 
Calculate: 
a) the applied stress SI 
b) the strain on the wire 
c)The Young modulus of steel.

Answer 11

a) 4 x 10^8
b) 0.2%
c) 2 x 10^11

Question 12

Young modulus of elasticity for cast Iron is 2.1 x 10^11 Pa.
It snaps when Me strain reaches 0.0005. What is the stress needed to break it? (Assume that it obeys Hooke’s law up to its breaking point.)

Answer 12

1.1 x 10^8

Question 13

A steel who is 6.0 m long and 1.6 mm in diameter. It is extended 1.0 mm by a force. The Young modulus of the steel is 2.0 x 10^11 Pa.

Answer 13

67N

Question 14

A piano wire made of steel (Young modulus = 2.0 x 10” Pa) has a length of 1.2 m and a diameter of 1.8mm. It stretches 2.5 mm when in tension.
Calculate the tension in the wire.
Find the extension of a copper wire of length 2.0 m and diameter 3.2 min when a force of 30N is applied. (Young modulus for copper = 110GPa)

Answer 14

1100N

6.8 x 10^-5