Question 1

A rock of mass $$m is $$twirled on a string in a horizontal plane at constant speed, as shown in the image. What is the work done by the tension in the string on the rock over one complete revolution?

Accepted Answer

Zero, because the tension is always perpendicular to the displacement.

Question 2

A 1 kg mass moves partway around a square loop 1 m on a side, ending 0.5 m below its starting position (see image). What is the work done by gravity during this journey? (Use $$g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$5\ \mathrm{J}$$

Question 3

A force $$F(x)$$ acts in the $$x-$$direction as shown in the graph: $$F = F_0$ for 0$$ \u003c x \u003c $$x_0/2$, and F = 2F_0$ for x_0$/2 \u003c x \u003c x_0$. What is the total work done by F$ as the object moves from x = 0$ to x$$ = $$x_0$$?

Accepted Answer

$$1.5 F_0$ x_0$

Question 4

A force $$F(x)$$ increases linearly from $$0 to$$ $$F_0 as$$ $$x$$ goes from $$0 to$$ $$x_f ($$see graph). What is the total work done by $$F(x)$$ from $$x = 0 to$$ $$x = x_f$$?

Accepted Answer

$$\frac{1}{2} F_0$ x_f$$

Question 5

A projectile is fired upward with initial speed $$v_0$$ and lands with speed $$v \u003c v_0$ due to air resistance (see image). What is the sign of the work done by air resistance during the flight?

Accepted Answer

Negative

Question 6

A child slides down three different frictionless ramps of the same height but different shapes (see image). How do their speeds at the bottom compare?

Accepted Answer

$$v_A = v_B = v_C$$

Question 7

In the collision shown, Ball 1 strikes stationary Ball 2 in a one-dimensional collision. If $$p_{1,i}$$ and $$p_{2,f}$$ are as shown, what is $$p_{1,f} in$$ 'graph units'?

Accepted Answer

-2

Question 8

A 1 kg mass moves partway around a square loop 1 m on a side, ending 0.5 m below its starting position (see image). If the mass instead took a long, winding path to the same final position, what would the work done by gravity be?

Accepted Answer

The same as before

Question 9

A rock of mass $$m is $$twirled on a string in a horizontal plane at constant speed (see image). What is the direction of the tension force relative to the instantaneous velocity of the rock?

Accepted Answer

Perpendicular to the velocity

Question 10

A hockey puck slides on ice at 1 m/s and comes to rest after moving 1 m on a carpet. If the puck had instead started at 2 m/s, how far would it travel on the carpet before stopping (assuming the same friction)?

Accepted Answer

4 m

Question 11

A box is being pulled up a rough incline by a rope connected to a pulley. Four forces act: tension ($$T$$), friction ($$f_k$$), gravity ($$F_g$$), and normal ($$N). $$What is the sign of the work done by each force?

Accepted Answer

$$W_T$$ (+), $$W_{f_k}$$ (-), $$W_{F_g} (0$$), $$W_N (0)$$

Question 12

A mass $$m is at $$the end of a light rod of length $$R$$, initially horizontal. What initial kinetic energy is required for the mass to pivot 270° to the vertical position and stop?

Accepted Answer

$$mgR$$

Question 13

A spring with spring constant $$k is $$stretched from $$x=0 to$$ $$x_f. $$What is the work done by the external force stretching the spring?

Accepted Answer

$$\frac{1}{2} k x_f^2$

Question 14

A car of mass $$m$$ moving with speed $$v on a $$level road slams on the brakes and skids to a stop. What is the work done by friction?

Accepted Answer

$$-\frac{1}{2} m v^2$

Question 15

A block slides from rest down a frictionless ramp and attains speed $$v at $$the bottom. To achieve a speed of $$2v at $$the bottom, how many times higher must the new ramp be?

Accepted Answer

4 times

Question 16

A cart rolls on a frictionless track. The total mechanical energy (KE + PE) is 45 kJ. What is the maximum kinetic energy the cart can have?

Accepted Answer

45 kJ

Question 17

Is it possible for the gravitational potential energy of an object to be negative?

Accepted Answer

Yes

Question 18

A mass slides down a rough ramp (with friction) of height $$h$$, starting from rest. While the mass is descending, its total mechanical energy (KE + PE)...

Accepted Answer

Decreases

Question 19

A car sits on the Earth's surface. Both are at rest. The car accelerates to a final velocity. After the car reaches $$v_{final}$$, the magnitude of the Earth's momentum is ________ the magnitude of the car's momentum.

Accepted Answer

The same as

Work, Energy, and Momentum: Study Notes for College Physics

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