Q: The work done by a conservative force is related to the change in potential energy by which equation?

$$W_{\text{cons}} = -\Delta U$$

Q: A 0.75-kg flower pot falls from a balcony that is 50 m above the street to a point 10 m above the ground. What is the change in gravitational potential energy?

$$\Delta U_g = 0.75 \times 9.8 \times (10 - 50) = -294 J$$

Q: A 10-kg box sits on a ledge 4 m above the ground. What is its gravitational potential energy relative to the ground?

$$U_g = 10 \times 9.8 \times 4 = 392 J$$

Q: A woman of mass 60 kg runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s. What is her power output?

$$P = \frac{(60 \times 9.8 \times 3.00) + (\frac{1}{2} \times 60 \times 2.00^2$)}{3.50} \approx 534 W$$

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

The work done by a conservative force is related to the change in potential energy by which equation?

Accepted Answer

$$W_{	ext{cons}} = -\Delta U$$

Question 3

A 0.75-kg flower pot falls from a balcony that is 50 m above the street to a point 10 m above the ground. What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U_g = 0.75 	imes 9.8 	imes (10 - 50) = -294 J$$

Question 4

Which of the following is NOT a type of potential energy mentioned in the study materials?

Accepted Answer

Frictional potential energy

Question 5

If a system is acted upon only by conservative forces, which of the following is true about its total mechanical energy?

Accepted Answer

It remains constant.

Question 6

A 10-kg box sits on a ledge 4 m above the ground. What is its gravitational potential energy relative to the ground?

Accepted Answer

$$U_g = 10 	imes 9.8 	imes 4 = 392 J$$

Question 7

Which equation correctly defines the gravitational potential energy near Earth's surface?

Accepted Answer

$$U_g = mgy$$

Question 8

Why is the change in gravitational potential energy independent of the path taken between two points?

Accepted Answer

Because the work done by gravity depends only on the vertical displacement.

Question 9

A rollercoaster starts from rest at height $$h. $$What must $$h be $$for the rollercoaster to make it around a loop of radius $$R ($$neglecting friction)?

Accepted Answer

$$h \geq \frac{5}{2}R$$

Question 10

Which of the following best describes the equilibrium point on a potential energy curve?

Accepted Answer

Where the slope of the potential energy curve is zero.

Question 11

For a spring with spring constant $$k$$, what is the potential energy stored when it is stretched by a distance $$x$$?

Accepted Answer

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

Question 12

A woman of mass 60 kg runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s. What is her power output?

Accepted Answer

$$P = \frac{(60 	imes 9.8 	imes 3.00) + (\frac{1}{2} 	imes 60 	imes 2.00^2$)}{3.50} \approx 534 W$$

Question 13

Which of the following is true about the work done by friction?

Accepted Answer

It is always negative.

Question 14

A 5.0 kg crate is pushed up a 20 m high, 20° ramp with a constant force of 25 N parallel to the ramp. The coefficient of kinetic friction is 0.17. If the crate starts from rest, what is the main energy principle used to find its speed at the top?

Accepted Answer

Conservation of mechanical energy, accounting for work done by non-conservative forces

Question 15

For a force $$F(x) in $$one dimension, the relationship between force and potential energy is:

Accepted Answer

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

Question 16

A system is said to be in stable equilibrium at a point $$x_0 if$$:

Accepted Answer

The potential energy $$U(x)$$ has a local minimum at $$x_0.$$

Question 17

If a box slides across a rough surface and comes to rest, what happens to its initial mechanical energy?

Accepted Answer

It is lost due to friction and transformed into thermal energy.

Question 18

Which of the following is a correct statement about the total mechanical energy $$E in a $$conservative system?

Accepted Answer

$$E = K + U$$ and is conserved.

Question 19

A particle moves in a potential $$U(x) = x^4$ - 4x^2$. At which value(s) of x$ is the equilibrium stable?

Accepted Answer

$$x = \pm 2$$

Potential Energy and Energy Conservation

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