Question 1

A mass of 0.400 kg is attached to a spring with force constant $$k = 12.0\ \mathrm{N/m} on a $$frictionless table. The mass is pulled back $$0.200\ \mathrm{m}$$ from equilibrium and released from rest. What is the speed of the block when it is at $$x = -0.125\ \mathrm{m}$$?

Accepted Answer

1.10 m/s

Question 2

Three planets A, B, and C orbit a star. $$M_A = M$$, $$M_B = 75M$$, $$M_C = 75M. $$Which is the correct relationship between their periods $$T$$?

Accepted Answer

$$T_B = T_C \u003e T_A$$

Question 3

Block A (12.0 kg) is on a rough table, connected by a rope over a disk-shaped pulley to a hanging block B (4.00 kg). The pulley has mass 5.00 kg. What coefficient of friction $$\mu$$ will cause block A to move at $$2.40\ \mathrm{m/s}$$ after sliding $$1.80\ \mathrm{m}$$?

Accepted Answer

0.0816

Question 4

A $$5.00\ \mathrm{kg}$$ mass oscillates at the end of a $$3.00\ \mathrm{m}$$ pendulum. If attached to a spring and oscillating at the same frequency, what is the spring constant $$k$$?

Accepted Answer

23.2 N/m

Question 5

An elevator (600 kg) must ascend 20.0 m in 12.0 s at constant speed. The motor provides up to 40 hp. If each passenger is 60.0 kg, what is the maximum number of passengers allowed? ($$1\ \mathrm{hp} = 750\ \mathrm{W})$$

Accepted Answer

30 passengers

Question 6

A box of mass $$m$$ slides down a frictionless ramp from height $$H = 4R$$ and enters a loop of radius $$R = 6.00\ \mathrm{m}. $$What is the normal force at the top of the loop (point B)?

Accepted Answer

$$4mg$$

Question 7

At the top of the loop (point B) in the previous problem, in what direction is the normal force acting on the box?

Accepted Answer

Down

Question 8

A passenger on the rim of a Ferris wheel (diameter 30 m) passes through the lowest point at $$3.00\ \mathrm{m/s}$$, gaining speed at $$0.500\ \mathrm{m/s^2$}. $$What is the magnitude and direction of the acceleration?

Accepted Answer

$$\vec{a} = 0.878\ \mathrm{m/s^2$} at$$ $$41.9^\circ$$ above the horizontal

Question 9

A tennis ball is launched and lands 40.0 m away, hitting a wall 6.00 m above the launch point after 3.50 s. What was the launch angle?

Accepted Answer

31.2 degrees

Question 10

A solid sphere rolls without slipping down a hill with a $$30^\circ$$ slope. $$\mu_s = 1.2$$, $$\mu_k = 0.8. $$Rank the forces: $$F_g ($$gravity), $$F_f ($$friction), $$F_N ($$normal).

Accepted Answer

$$F_g \u003e F_N \u003e F_f$$

Question 11

A police car is at rest when a speeder passes at $$40.0\ \mathrm{m/s}. $$The cop starts after $$1.50\ \mathrm{s}$$ and catches the speeder $$13.0\ \mathrm{s}$$ after the speeder passed. What is the cop's acceleration?

Accepted Answer

2.46 m/s$$^2$$

Question 12

Match the position curves (a)-(c) with their corresponding acceleration curves (i)-(iii):

Accepted Answer

(a) with (iii), (b) with (i), (c) with (ii)

Question 13

Block A ($$3.00\ \mathrm{kg}$$, $$\vec{v}_A = 4.00\hat{i} + 5.00\hat{j}) $$and block B ($$4.00\ \mathrm{kg}$$, $$\vec{v}_B = -4.00\hat{i} - 3.00\hat{j}) $$collide completely inelastically. What is their speed after collision?

Accepted Answer

1.36 m/s

Question 14

A person of mass $$M$$ stands at the end of a uniform diving board (mass $$m$$, length $$L). $$Two braces are at the edge and at $$0.2L. $$What is the force on brace A?

Accepted Answer

$$(1.5m + 4M)g$$, up

Question 15

An Atwood's machine uses a solid sphere, a solid disk, or a thin-walled hollow cylinder as the pulley. Rank the total kinetic energy $$K_{tot}$$ when mass $$2m$$ hits the ground.

Accepted Answer

$$K_{tot,a} \u003e K_{tot,b} \u003e K_{tot,c}$$

Question 16

Four identical masses $$M$$ and a fifth mass $$m$$ are arranged as shown. What is the magnitude of the gravitational force on $$m$$ due to the others?

Accepted Answer

$$2GmM/a^2$$

Question 17

A blu-ray disc slows from $$250\ \mathrm{rad/s} to$$ $$150\ \mathrm{rad/s}$$ under a constant torque $$2.88 	imes 10$$^{-4}$$\ \mathrm{Nm}$$, with $$I = 3.60 	imes 10$$^{-5}$$\ \mathrm{kg\cdot m^2$}. $$How many revolutions does it complete during this change?

Accepted Answer

398 revolutions

Question 18

A ball is attached to a string and rotated in a vertical circle. At the bottom of the path, which free-body diagram is correct?

Accepted Answer

Diagram A

Question 19

A window washer pushes his 12.0 N brush up a vertical window at constant speed using a light rod at $$53.1^\circ to $$the horizontal. The coefficient of kinetic friction is $$\mu_k = 0.150. $$What is the magnitude of the force $$\vec{F}$$ applied?

Accepted Answer

16.9 N

Forces and Friction on an Inclined Rod (Window Washer Problem)

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