Young Modulus

State the breaking stress of this copper wire.

Answer explanation

1.9 × 10⁸ Pa

Define tensile strain.

Answer explanation

Extension divided by its original length. Do use symbols unless they are defined. Strain has no units.

Give the (x,y) coordinates of a point on the line where you consider plastic deformation may start.

Answer explanation

Your x-coordinate should be between a strain of 1.0 × 10⁻³ and 3.5 × 10⁻³ .

Use the graph to calculate the Young modulus of copper. State an appropriate unit for your answer.

Answer explanation

Ensure you have clear evidence of gradient calculation for straight section eg 1.18 (1.2) × 10⁸ /1.0 × 10⁻³

= 120 GPa and stress used > 0.6 × 10⁸ Pa

Allow range 116 − 120 GPa Pa or Nm⁻² or N/m²

(e) The area under the line in a stress-strain graph represents the work done per unit volume to stretch the wire.

(i) Use the graph to find the work done per unit volume in stretching the wire to a strain of 3.0 × 10^–3 .

Answer explanation

(e) (i) ensure you have made a clear attempt to calculate correct area

(evidence on graph is sufficient)

(32 whole squares + 12 part/2 = 38 squares)

(38 × 10000 = ) 380000 (J m⁻³ )

allow range 375000 to 400000 (Jm^-3)

(ii) Calculate the work done to stretch a 0.015 kg sample of this wire to a strain of 3.0 × 10^–3 .

The density of copper = 8960 kg m^–3

Answer explanation

(ii) V = m/ρ or

0.015/8960 or 1.674 × 10⁻⁶ (m³ )

380 000 × 1.674 × 10⁻⁶

= 0.64 (0.6362 J)

error carried forward from ei

Climbing ropes are designed to be able to withstand large impact forces without breaking.

What material property describes such a rope?

Answer explanation

Tough (1)

The graph shows the characteristics of a climbing rope when stretched up to its breaking point.

Answer the following:

The extension at the limit of proportionality, P

The force at E, a possible point for the elastic limit

Answer explanation

P occurs at end of straight line section

[allow 2.6 – 2.8 m extension] (1)

E: accept value between P and maximum force value (1)

If P not shown allow 2.6 – maximum force value]

Calculate the stiffness k of the rope.

Answer explanation

k = F/x;

k = gradient of graph (1)

= 7 kN ÷ 2.25 m

= 3.1 kNm^–1 (1)

The original length of the rope is 50 m.

Calculate the breaking strain of the rope.

Answer explanation

From graph, maximum extension = 3.4 m (1) Breaking strain = 3.4/50 = 0.07 (0.068 or 6.8%) (1) 2 [allow ecf. from extension]