Question 1

Which of the following statements best describes a conservative force?

Accepted Answer

A force for which the work done depends only on the initial and final positions, not the path taken.

Question 2

A block slides down a frictionless incline of height $$h. $$What is its velocity at the bottom?

Accepted Answer

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

Question 3

If a block of mass $$m is $$dropped from a height $$h$$ with an initial velocity $$v_i$$, what is its velocity at the bottom?

Accepted Answer

$$v_f = \sqrt{2gh + v_i^2$}$$

Question 4

Which of the following is true about the normal force on an object sliding down an incline?

Accepted Answer

It is perpendicular to the direction of motion and does no work.

Question 5

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

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

Question 6

An archer pulls back a bowstring by a distance $$x$$, storing energy in the bow modeled as a spring with constant $$k. If $$the arrow has mass $$m$$, what is its velocity when released?

Accepted Answer

$$v = x\sqrt{\frac{k}{m}}$$

Question 7

If an archer shoots six arrows at once, each with mass $$m$$, using the same draw distance $$x$$ and spring constant $$k$$, how far will each arrow travel compared to a single arrow?

Accepted Answer

Each arrow will travel 1/6 of the distance.

Question 8

A ball of mass $$m$$ collides elastically with a spring attached to a wall. If the ball's initial speed is $$v$$, what is the maximum compression $$x of $$the spring (spring constant $$k$$)?

Accepted Answer

$$x = \sqrt{\frac{mv^2$}{k}}$$

Question 9

Which equation correctly relates the force $$F$$ exerted by a spring to its displacement $$x$$?

Accepted Answer

$$F = -kx$$

Question 10

A roller coaster car starts at rest at height $$h_A$$ and descends to height $$h_B$$ with no friction. What is its speed at $$h_B$$?

Accepted Answer

$$v_B = \sqrt{2g(h_A - h_B)}$$

Question 11

Which of the following is NOT a property of mechanical energy in a system with only conservative forces?

Accepted Answer

Mechanical energy can be transformed into heat.

Question 12

A block slides down a rough incline with friction. Which statement is true about its mechanical energy?

Accepted Answer

Mechanical energy is transformed into heat due to friction.

Question 13

Which formula gives the maximum range $$R_{max} of a $$projectile launched with velocity $$v_0 at $$angle $$	heta = 45^\circ ($$neglecting air resistance)?

Accepted Answer

$$R_{max} = \frac{v_0$^2}{g}$$

Question 14

Which of the following is a correct statement about the work done by friction?

Accepted Answer

It transforms mechanical energy into heat.

Question 15

If the potential energy $$U of a $$system is known as a function of position $$x$$, how can the force $$F be $$found?

Accepted Answer

$$F = -\frac{dU}{dx}$$

Question 16

A pendulum is released from rest at height $$h. $$What is its speed at the lowest point?

Accepted Answer

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

Question 17

Which of the following is true about the potential energy of a spring?

Accepted Answer

It is zero when the spring is at equilibrium.

Question 18

A block of mass $$m$$ slides down a frictionless incline of angle $$	heta$$ and height $$h. $$What is the work done by gravity?

Accepted Answer

$$W = mgh$$

Question 19

Which of the following is a correct statement about energy conservation in the presence of non-conservative forces?

Accepted Answer

Total energy is conserved, but mechanical energy may not be.

Question 20

A ball of mass $$m is $$dropped from height $$h$$ and bounces elastically off a spring. What is its speed just after leaving the spring?

Accepted Answer

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

Module 11: Potential Energy and Conservation of Mechanical Energy

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