Question 1

A spring with a spring constant $$k = 100\ \mathrm{N/m} is $$compressed by $$0.2\ \mathrm{m}$$ from its equilibrium position. What is the elastic potential energy stored in the spring?

Accepted Answer

$$2\ \mathrm{J}$$

Question 2

Which of the following statements about Hooke's Law is correct?

Accepted Answer

The force exerted by a spring is proportional to the displacement from equilibrium and acts in the opposite direction.

Question 3

A bungee cord behaves like a spring with $$k = 50\ \mathrm{N/m}. If a $$jumper stretches the cord by $$3\ \mathrm{m}$$, what is the magnitude of the force exerted by the cord?

Accepted Answer

$$150\ \mathrm{N}$$

Question 4

If a spring is neither stretched nor compressed, which of the following is true?

Accepted Answer

The spring is at its equilibrium position and stores no elastic potential energy.

Question 5

A student stretches a spring by $$0.5\ \mathrm{m}$$ and measures a restoring force of $$10\ \mathrm{N}. $$What is the spring constant $$k$$?

Accepted Answer

$$20\ \mathrm{N/m}$$

Question 6

Which of the following devices does NOT store elastic potential energy as described in the study materials?

Accepted Answer

A spinning wheel

Question 7

A spring with $$k = 200\ \mathrm{N/m} is $$stretched by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$1\ \mathrm{J}$$

Question 8

If the spring constant $$k of a $$spring is doubled, but the displacement $$x$$ remains the same, how does the elastic potential energy change?

Accepted Answer

It is doubled.

Question 9

A trampoline acts like a spring with $$k = 500\ \mathrm{N/m}. If a $$child compresses it by $$0.2\ \mathrm{m}$$, what is the force exerted by the trampoline?

Accepted Answer

$$100\ \mathrm{N}$$

Question 10

Which of the following best describes the relationship between the spring force and displacement according to Hooke's Law?

Accepted Answer

The force is directly proportional to displacement.

Question 11

A spring is stretched by $$x$$ meters. Which equation gives the elastic potential energy $$U_s$$ stored in the spring?

Accepted Answer

$$U_s = \frac{1}{2}kx^2$

Question 12

A 'stiff' spring is characterized by which of the following?

Accepted Answer

A large spring constant $$k$$

Question 13

A spring is compressed by $$0.3\ \mathrm{m}$$ and stores $$1.35\ \mathrm{J} of $$elastic potential energy. What is the spring constant $$k$$?

Accepted Answer

$$30\ \mathrm{N/m}$$

Question 14

If a spring is stretched by $$x$$ and then compressed by $$x$$, how does the elastic potential energy compare in both cases?

Accepted Answer

It is the same in both cases.

Question 15

A rubber band is stretched and then released. Which energy transformation primarily occurs?

Accepted Answer

Elastic potential energy to kinetic energy

Question 16

A spring with $$k = 40\ \mathrm{N/m} is $$stretched by $$0.5\ \mathrm{m}. $$What is the force exerted by the spring?

Accepted Answer

$$20\ \mathrm{N}$$

Question 17

Which of the following real-life scenarios best illustrates the concept of elastic potential energy?

Accepted Answer

A compressed spring in a toy car launcher

Question 18

If the displacement of a spring is tripled, how does the elastic potential energy stored in the spring change?

Accepted Answer

It becomes nine times greater.

Question 19

A spring is stretched by $$0.4\ \mathrm{m}$$ and the force measured is $$8\ \mathrm{N}. $$What is the value of the spring constant $$k$$?

Accepted Answer

$$20\ \mathrm{N/m}$$

Question 20

Which of the following best explains why the elastic potential energy is always positive, regardless of whether the spring is stretched or compressed?

Accepted Answer

Because the energy depends on the square of the displacement, which is always positive.

Elastic Potential Energy and Hooke's Law

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