12 the StReNGth OF MAteRIALS
PRACTICE QUESTIONS 1. A type of exercise device is used to provide resistive forces when a person applies compressive forces to its handles. The stiff spring inside the device compresses as shown in Figure Q1. spring
force exerted by person
ii. The person causes a compression of 0.28 m in a time of 1.5 s. Use the graph in part a to calculate the average power developed. AQA Unit 2 January 2011 Q1
compression metal tubes handles
Explain how this formula can be derived from a graph of force against extension.
L
force exerted by person
2. A cable-car system is used to transport people up a hill. Figure Q3 shows a stationary cable car suspended from a steel cable of cross-sectional area 2.5 × 10–3 m2. cable
Figure Q1
a. The force exerted by the spring over a range of compressions was measured. The results are plotted on the grid in Figure Q2.
cable car
Figure Q3
500
a. The graph in Figure Q4 is for a 10 m length of this steel cable. Use the graph to calculate the initial gradient, k, for this sample of the cable.
300 200
3.0
100
2.5
0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Compression, L / m Figure Q2
i.
State Hooke’s law.
ii. State which two features of the graph confirm that the spring obeys Hooke’s law over the range of values tested. iii. Use the graph to calculate the spring constant, stating an appropriate unit. b. i. The formula for the energy stored by the spring is E=
1 2
Load / 105 N
Force / N
400
2.0 1.5 1.0 0.5 0.0 0.0
1.0
2.0 3.0 4.0 5.0 Extension / 10−3 m
6.0
7.0
Figure Q4
F ΔL
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