5.6 Stretching springs: Hooke's law
10 exam questions worth 25 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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What is the unit of the spring constant?
Choose one answer.
Correct Not quite: the answer is N/m
Mark scheme
B: N/m
Model answer
N/m (B).
A spring has a natural length of 8.0 cm. When a load is added its length becomes 11.0 cm. Calculate the extension in metres.
Mark scheme
extension = 11.0 − 8.0 = 3.0 cm (1); 0.030 m (1)
Model answer
Extension = 11.0 − 8.0 = 3.0 cm = 0.030 m.
A force of 6.0 N stretches a spring by 0.030 m. Calculate the spring constant.
Mark scheme
k = F ÷ e (1); 6.0 ÷ 0.030 (1); 200 N/m (1)
Model answer
k = F / e = 6.0 / 0.030 = 200 N/m.
A spring has a spring constant of 25 N/m. Calculate the force needed to stretch it by 12 cm.
Mark scheme
e = 0.12 m (1); F = k e = 25 × 0.12 (1); 3.0 N (1)
Model answer
e = 0.12 m. F = k e = 25 × 0.12 = 3.0 N.
A spring with a spring constant of 80 N/m is stretched by 0.10 m. Calculate the energy stored in the spring.
Mark scheme
E = ½ k e² (1); ½ × 80 × 0.10² (1); 0.40 J (1)
Model answer
E = ½ k e² = 0.5 × 80 × 0.10² = 0.40 J.
State the difference between elastic deformation and inelastic deformation.
Mark scheme
elastic: the object returns to its original shape when the force is removed (1); inelastic: the object is permanently deformed / does not return to its original shape (1)
Model answer
An elastically deformed object returns to its original shape when the forces are removed. An inelastically deformed object is permanently changed.
Describe what the force-extension graph for a spring shows about the relationship between force and extension, up to and beyond the limit of proportionality.
Mark scheme
up to the limit it is a straight line through the origin (1); so force is directly proportional to extension (1); beyond the limit, the graph curves / the extension is no longer proportional to the force (1)
Model answer
Up to the limit of proportionality the graph is a straight line through the origin, so force is directly proportional to extension. Beyond the limit the graph curves, so they are no longer proportional.
A student stretches a spring beyond its limit of proportionality and then releases it. Describe what is likely to happen to the length of the spring, and explain why.
Mark scheme
the spring does not return to its original length / is longer than before (1); it has been permanently / inelastically deformed (1)
Model answer
The spring will not return to its original length because it has been permanently (inelastically) deformed.
The graph of force against extension for a spring is a straight line through the origin with a gradient of 50 N/m. State what the gradient represents and calculate the force needed for an extension of 0.20 m.
Mark scheme
the gradient is the spring constant (1); F = k e = 50 × 0.20 (1); 10 N (1)
Model answer
The gradient is the spring constant. F = k e = 50 × 0.20 = 10 N.
Explain, using ideas about energy, what happens when a stretched spring is released and a toy car attached to it moves forward.
Mark scheme
work was done to stretch the spring and energy is stored in the elastic potential store (1); when released, the energy is transferred from the elastic potential store (1); to the kinetic energy store of the car (and some to thermal stores by friction) (1)
Model answer
Work done in stretching the spring stores energy in its elastic potential store. When it is released, this energy is transferred to the kinetic store of the toy car, with some being dissipated as thermal energy because of friction.
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