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, $$\Delta U_g$$, of the pot? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

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

Q: A 10-kg box sits on a ledge 4 m above the ground. What is its gravitational potential energy relative to the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$U_g = 10 \times 9.8 \times 4 = 392\ \mathrm{J}$$

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? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Power $$= \frac{mgh + \frac{1}{2}mv^2$}{t} = \frac{60 \times 9.8 \times 3 + 0.5 \times 60 \times 2^2$}{3.5} = 540\ \mathrm{W}$$

Question 1

Which of the following statements about conservative forces is TRUE?

Accepted Answer

For conservative forces, the work done only depends on the initial and final positions, not the path.

Question 2

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, $$\Delta U_g$$, of the pot? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 3

Which equation correctly expresses the work done by a constant force $$\vec{F}$$ over a displacement $$\Delta \vec{x}$$?

Accepted Answer

$$W = \vec{F} \cdot \Delta \vec{x}$$

Question 4

A box of mass $$m is $$dropped from a height $$h$$ above the ground. What is its gravitational potential energy just before it hits the ground, assuming $$y=0 at $$ground level?

Accepted Answer

$$U_g = 0$$

Question 5

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

Accepted Answer

Kinetic energy

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? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$U_g = 10 	imes 9.8 	imes 4 = 392\ \mathrm{J}$$

Question 7

Which statement best describes the path independence of potential energy change for conservative forces?

Accepted Answer

The change in potential energy depends only on the initial and final positions.

Question 8

For a non-constant force $$F(x)$$ acting along the $$x-$$axis, which integral gives the work done from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F(x) dx$$

Question 9

A rollercoaster starts from rest at height $$h$$ and must make it around a loop of height $$H. $$Neglecting friction, what is the minimum value of $$h$$ required?

Accepted Answer

$$h = 2H$$

Question 10

Which of the following is TRUE about the force of friction?

Accepted Answer

There is no potential energy associated with friction.

Question 11

If a system is acted upon only by conservative forces, which of the following is conserved?

Accepted Answer

Total mechanical energy ($$E = K + U)$$

Question 12

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 13

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

Accepted Answer

$$U_g = mgy$$

Question 14

A system is in equilibrium when which condition is met on the energy curve $$U(x)$$?

Accepted Answer

$$\frac{dU}{dx} = 0$$

Question 15

What is the relationship between the force $$F(x)$$ and the potential energy $$U(x) in $$one dimension?

Accepted Answer

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

Question 16

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

Accepted Answer

$$U_s = \frac{1}{2} k x^2$

Question 17

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? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Power $$= \frac{mgh + \frac{1}{2}mv^2$}{t} = \frac{60 	imes 9.8 	imes 3 + 0.5 	imes 60 	imes 2^2$}{3.5} = 540\ \mathrm{W}$$

Question 18

If a box slides across a rough surface and comes to a stop due to friction, what happens to its mechanical energy?

Accepted Answer

It is converted into thermal energy due to friction.

Question 19

Given the potential energy function $$U(x) = x^4$ - x^2$, at which value(s) of x$ is the equilibrium stable?

Accepted Answer

$$x = \pm 1/\sqrt{2}$$

Potential Energy and Energy Conservation: Study Notes

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