Question 1

Which of the following best describes a conservative force?

Accepted Answer

A force for which the work done over any closed path is zero.

Question 2

A 2.0 kg object is lifted from the ground to a height of 5.0 m. What is the change in its gravitational potential energy? Use $$g = 9.8 \mathrm{\ m/s^2$}.$$

Accepted Answer

$$\Delta U_g = 98 \mathrm{\ J}$$

Question 3

Which equation correctly relates the work done by gravity to the change in gravitational potential energy when an object is raised?

Accepted Answer

$$W_g = -\Delta U_g$$

Question 4

A spring with force constant $$k = 200 \mathrm{\ N/m} is $$compressed by $$x = 0.10 \mathrm{\ m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_{el} = 0.5 \mathrm{\ J}$$

Question 5

Which of the following is NOT a property of a conservative force?

Accepted Answer

The work done depends on the path taken.

Question 6

A block of mass $$m$$ slides down a frictionless ramp from height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 7

If a nonconservative force such as friction acts on a system, which statement is true about the system's mechanical energy?

Accepted Answer

Mechanical energy is not conserved; some is transformed into internal energy.

Question 8

A trapeze artist of mass $$m$$ swings from rest at an angle $$\$$theta_0$$ with ropes of length L$. What is her speed at the lowest point?

Accepted Answer

$$v = \sqrt{2gL(1-\cos\$$theta_0$$)}$$

Question 9

Which of the following best explains why the total work done by gravity over a closed path is zero?

Accepted Answer

Gravity is a conservative force, so the work done depends only on the endpoints, not the path.

Question 10

A block of mass $$m is $$pushed by a spring (force constant $$k) $$compressed by $$x$$ and then slides across a table with friction ($$\mu) $$for distance $$d$$ before falling height $$h. $$What is the speed when it lands?

Accepted Answer

$$v = \sqrt{\frac{kx^2$}{m} + 2gh - 2\mu gd}$$

Question 11

Which formula gives the elastic potential energy stored in a spring?

Accepted Answer

$$U_{el} = \frac{1}{2}kx^2$

Question 12

In the context of energy diagrams, what does a point of stable equilibrium correspond to?

Accepted Answer

A minimum in the potential energy curve.

Question 13

Which of the following is true about the work done by friction over a closed path?

Accepted Answer

It is always negative.

Question 14

A hiker climbs a mountain with steep slopes. What does a large gradient in gravitational potential energy indicate?

Accepted Answer

A strong force pushing the hiker toward lower elevation.

Question 15

Which equation expresses the conservation of mechanical energy for an isolated system with only conservative forces?

Accepted Answer

$$K_i + U_i = K_f + U_f$$

Question 16

A ball is thrown from a height $$h$$ with speed $$v_0 at an $$angle. Neglecting air resistance, what is its speed when it returns to height $$h$$?

Accepted Answer

$$v = v_0$

Question 17

Which of the following is a real-world example of energy storage using gravitational potential energy?

Accepted Answer

Pumping water to a higher elevation reservoir in a hydroelectric power plant.

Question 18

For a conservative force in one dimension, how is the force related to the potential energy function $$U(x)$$?

Accepted Answer

$$F(x) = -\frac{dU}{dx}$$

Question 19

Which statement about elastic potential energy is correct?

Accepted Answer

Elastic potential energy is never negative.

Question 20

A roller coaster starts from rest at height $$h. $$Neglecting friction, what is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Potential Energy and Energy Conservation (Chapter 7 Study Notes)

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