Question 1

Which of the following best describes a conservative force?

Accepted Answer

A force for which the work done depends only on the starting and ending points, not the path taken.

Question 2

A spring with force constant $$k = 200\ \mathrm{N/m} is $$compressed by $$x = 0.05\ \mathrm{m}. $$What is the potential energy stored in the spring?

Accepted Answer

$$0.125\ \mathrm{J}$$

Question 3

Which equation correctly expresses the conservation of mechanical energy for a system with only conservative forces?

Accepted Answer

$$KE_i + PE_i = KE_f + PE_f$$

Question 4

A 0.1 kg toy car is launched by compressing a spring (force constant $$k = 250\ \mathrm{N/m}) by$$ $$0.04\ \mathrm{m}. $$Assuming no friction, what is the car's speed just after leaving the spring?

Accepted Answer

$$3.2\ \mathrm{m/s}$$

Question 5

Which of the following is NOT a characteristic of potential energy?

Accepted Answer

It depends on the path taken between two points.

Question 6

A guitar string is pulled a distance $$d$$ and released. Which equation best describes the potential energy stored in the string, assuming it behaves like a spring?

Accepted Answer

$$PE = \frac{1}{2}kd^2$

Question 7

If the only forces acting on a system are conservative, what happens to the total mechanical energy?

Accepted Answer

It remains constant.

Question 8

A block slides down a frictionless ramp and compresses a spring at the bottom. Which of the following statements is true?

Accepted Answer

The sum of the block's kinetic and the spring's potential energy is constant.

Question 9

Which of the following is an example of a non-conservative force?

Accepted Answer

Friction

Question 10

In the Energy Skate Park simulation, what happens to the skater's total mechanical energy if friction is present?

Accepted Answer

It decreases as some energy is converted to thermal energy.

Question 11

A spring is stretched by $$x$$ meters. What is the work done by the spring force?

Accepted Answer

$$W = -\frac{1}{2}kx^2$

Question 12

A mass is attached to a spring and oscillates back and forth. At the maximum compression, what is true about the energies?

Accepted Answer

Kinetic energy is zero and potential energy is maximum.

Question 13

Which of the following equations represents Hooke's Law?

Accepted Answer

$$F = kx$$

Question 14

A 0.2 kg mass is dropped from a height of 2 m onto a spring with $$k = 500\ \mathrm{N/m}. $$What is the maximum compression $$x of $$the spring? (Neglect air resistance.)

Accepted Answer

$$x = 0.28\ \mathrm{m}$$

Question 15

If a skater in the Energy Skate Park simulation starts at a higher reference height, what happens to their maximum kinetic energy?

Accepted Answer

It increases because the potential energy at the top is greater.

Question 16

Which of the following best explains why the area under the force vs. displacement graph for a spring is $$\frac{1}{2}kx^2$?

Accepted Answer

Because the force increases linearly with displacement, forming a triangle under the graph.

Question 17

A bungee cord behaves like a spring with $$k = 40\ \mathrm{N/m}. If a $$jumper stretches it by $$2\ \mathrm{m}$$, how much energy is stored in the cord?

Accepted Answer

$$80\ \mathrm{J}$$

Question 18

Which of the following statements about mechanical energy is correct?

Accepted Answer

Mechanical energy is the sum of kinetic and potential energy.

Question 19

A mass attached to a spring is pulled and released. If the system is frictionless, what happens to the total energy over time?

Accepted Answer

It remains constant, oscillating between kinetic and potential forms.

Question 20

In a real-world scenario, why does a skater eventually stop moving in the Energy Skate Park simulation if friction is included?

Accepted Answer

Because mechanical energy is transformed into thermal energy due to friction.

Conservative Forces and Potential Energy: Springs, Mechanical Energy, and Conservation

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