Q: A projectile is fired up with initial speed $$v_0$$ through air. Later, it comes down and has a final speed $$v \u003c v_0$. Air resistance is NOT negligible. What was the sign of the work done by friction during the flight?

$$W_{\text{friction}} \u003c 0$$

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

Question 2

A 1 kg mass moves partway around a square loop 1 m on a side, ending 0.5 m below its original 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

Suppose the same 1 kg mass is taken on a long, winding journey but ends at the same final position as before (0.5 m below the start). What is the total work done by gravity?

Accepted Answer

It is the same as before

Question 4

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

Accepted Answer

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

Question 5

A force is applied in the $$x-$$direction while an object moves a distance $$x_0 on $$the $$x-$$axis. The force varies with position as shown in the graph (step function). What is the total work done by $$F$$?

Accepted Answer

$$1.5 F_0$ x_0$

Question 6

Now suppose the force varies with position as shown in the graph (a straight line from $$(0,0) to$$ $$(x_f, F_0$)). $$What is the total work done by $$F(x)$$ going from $$0 to$$ $$x_f$$?

Accepted Answer

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

Question 7

Marie Curie lowers a book of mass $$m$$ downward a distance $$h at $$constant speed $$v. $$What is the work done by the force of gravity?

Accepted Answer

Positive

Question 8

Marie Curie lowers a book of mass $$m$$ downward a distance $$h at $$constant speed $$v. $$What is the work done by the force of Marie’s hand?

Accepted Answer

Negative

Question 9

Marie Curie lowers a book of mass $$m$$ downward a distance $$h at $$constant speed $$v. $$What is the total work done on the book?

Accepted Answer

Zero

Question 10

You toss a ball into the air and catch it again at the same position. What is the total work done by the gravitational force during the flight?

Accepted Answer

$$W_{	ext{grav}} = 0$$

Question 11

Is kinetic friction a conservative force?

Accepted Answer

No

Question 12

A projectile is fired up with initial speed $$v_0$$ through air. Later, it comes down and has a final speed $$v \u003c v_0$. Air resistance is NOT negligible. What was the sign of the work done by friction during the flight?

Accepted Answer

$$W_{	ext{friction}} \u003c 0$$

Question 13

A hockey puck slides on an ice rink at $$1\ \mathrm{m/s}$$ when it slides onto a carpet. How much more kinetic energy would the puck have started with if it was initially moving at $$2\ \mathrm{m/s}$$ instead?

Accepted Answer

Four times as much

Question 14

A hockey puck slides on an ice rink at $$1\ \mathrm{m/s}$$ when it slides onto a carpet and comes to rest after moving $$1\ \mathrm{m} on $$the carpet. How far along the carpet would the puck go if its initial speed were $$2\ \mathrm{m/s}$$? (Assume the same friction force.)

Accepted Answer

$$4\ \mathrm{m}$$

Question 15

Car 1 and car 2 have the same mass, but car 1 is going twice as fast. How do their kinetic energies compare?

Accepted Answer

$$KE_1 = 4$$ $$KE_2$$

Question 16

Car 1 has twice the mass of car 2 but both have the same kinetic energy. How do their speeds compare?

Accepted Answer

$$v_2 = 2$$ $$v_1$$

Question 17

What is the work required to stretch an ideal spring from $$x=0 to$$ $$x_f$$?

Accepted Answer

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

Question 18

What is the definition of power in terms of work and time?

Accepted Answer

$$P = \frac{W}{t}$$

Work, Energy, and the Work-Energy Theorem

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