The Young Modulus (AQA AS Physics)

An experiment was carried out to find the Young Modulus of copper, using copper wire.

The uncertainties in the measurements are given below.

measurement	uncertainty
applied load
diameter of wire
extension
original length of wire

What is the percentage uncertainty in the Young Modulus applied to the wire?

A metal tube with a thin wall thickness w is shown in the diagram. The thickness of the wall is small when compared to the diameter of the tube.

A force T applied parallel to the axis of the tube puts the tube under tension. It is proposed that making the wall thicker would reduce the stress on the tube.

 If the tube diameter and the tension remain the same, which wall thickness would half the stress?

A steel metal wire has the following properties:

                                                 diameter = 5.0 × 10^–4 m

                                        Young modulus = 2.0 × 10¹¹ Pa

                                                      tension = 20 N

The string snaps and contracts elastically.

By what percentage does a length of a piece of the string contract?

The Young modulus of a metal wire is dependent on which property?

The Young modulus E and the force per unit extension k describes the behaviour of a wire under tensile stress.

For a wire of length L and cross-sectional area A, what is the relationship between E and k?

A steel bar, shown in the diagram, has a circular cross-section that is under tension T.

The diameter of the thinner portion is half the wider portion.

What is the value of   ?

A student wanted to find the young modulus of a wire. The equation for the young modulus E is:

The student extended the wire with a known force and made a series of measurements.

Which measurement has the largest effect on the uncertainty in the value of the calculated Young modulus?

	measurement	symbol	value
A	length of wire before force applied	l	2.043 ± 0.002 m
B	force applied	F	19.62 ± 0.01 N
C	extension of wire with force applied		5.2 ± 0.2 mm
D	diameter of wire	d	0.54 ± 0.02 mm

Which unit cannot be used for the Young Modulus?

The stress-strain graph for carbon is shown.

What is the Young Modulus of the carbon?

A steel wire X has a length L and a circular cross-section of radius r. When X hands vertically and a load is attached to the bottom end, it extends by e.

Another wire Y is made from the same material and has the same load attached to it.

Which length and radius for Y will produced an extension of ?

A construction site crane has a steel lifting cable with diameter 36 mm and length 27.0 m. The steel used has a Young modulus of 200 GPa.

Calculate the extension when the crane is used to lift materials with weight 28 kN.

Steel has a Young Modulus of 2 ×  Pa and a breaking strain of 0.1 %.

What is the force needed to break a steel wire of diameter 1 mm?

The graph shows the behaviour of a copper alloy when it is stressed.

Which of the following shows a second line for a material which;

• is brittle,
• has a Young modulus lower than the copper alloy
• fractures at a strain of 2.6 x ?

Two springs are connected in series as shown. The values of the spring constants are different, where k₁ = 25 N cm⁻¹ and k₂ = 35 N cm⁻¹.

The spring has a circular cross-sectional area of 707 mm² and before the 50 N load is placed, the combination have a length of 5.0 cm.

What is the young modulus of the material that the spring is made from?

An A Level Physics student carries out an investigation into the Young Modulus of a copper wire and plots her graph as shown.

How would the graph be different if she repeated the experiment, first with thinner wire, and then using thicker wire?

A popular playground ride is a rocking horse on a spring, as shown. The toy is designed to be used by children aged between 2-5 years old.

When the child sits on the horse, the spring should compress a little but not too much for play to be both fun, and safe.

Clinical data from childcare professionals suggests that 2 year old children have average weight of 12.0 kg, while five-year old children average 19.0 kg.

Which spring constant would be most suitable?

The system below shows a composite rod made from two different materials.

The dimensions and Young Modulus for each rod are as follows:

What is the ratio of ?

The supporting cable of a suspension footbridge if the cable has a diameter of 55 mm, and it exerts an upwards force on the footpath of 5.2 kN.

If the Young Modulus of the steel the cable is made from is 2.0 GPa, and the maximum strain the cable can withstand before breaking is 5.0 %, then what is the breaking stress?

A uniform, heavy chain of Young Modulus, E, length, L, mass per unit length, μ, cross-sectional area, A is supported by a thin rope with negligible mass.

Find an expression for the extension, ΔL, when the chain is fully suspended above the ground.

A copper wire of length 1.80 m and cross-sectional area of 1.6 x m² is put under a tensile stress of 2.45 N. The length of the wire increases by 2 mm.

The experiment has been done using the following equipment:

• metre ruler to measure length
• vernier scale with precision of 0.1 mm to measure extension
• micrometer to measure diameter of the wire

What is the Young Modulus of copper? You can assume the value for applied force is correct.