Young Modulus

State the breaking stress of this copper wire.

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Answer explanation

1.9 × 10⁸ Pa

Define tensile strain.

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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.

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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.

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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 .

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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

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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?

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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

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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.

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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.

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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]