Q: A crate of mass $$m is $$pushed at constant speed up a rough incline of angle $$\theta. $$The coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the friction force?

$$F_{fric} = \mu_k m g \cos\theta$$

Question 1

A 3 kg child and her sled are released from rest at the top of a frictionless hill of height $$h_i$$ and slide down to compress a spring of force constant $$k = 75\ \mathrm{N/m} at $$the bottom. If the initial height is $$h_i = 4\ \mathrm{m}$$ and the initial speed is $$v_i = 3\ \mathrm{m/s}$$, what is the maximum compression $$x_f of $$the spring? (Ignore friction and air resistance.)

Accepted Answer

$$x_f = 0.89\ \mathrm{m}$$

Question 2

A ball is attached to a spring and moves in a horizontal circle on a frictionless surface. The spring obeys Hooke's Law. After one complete revolution, what is the net work done by the spring force on the ball?

Accepted Answer

$$W = 0$$

Question 3

A block of mass $$m is $$attached to a string and hangs vertically. The tension in the string is $$T. $$Which of the following statements is correct regarding the forces acting on the block at rest?

Accepted Answer

The weight and the tension force are equal in magnitude and opposite in direction because the net force must sum to zero by Newton's second law.

Question 4

A block of mass $$m is $$connected by a light string over a frictionless pulley to a block of mass $$4m as $$shown. What is the acceleration $$a of $$the heavier block?

Accepted Answer

$$a = \dfrac{3}{5}g$$

Question 5

A crate of mass $$m is $$pushed up a rough incline at constant speed. The coefficient of kinetic friction is $$\mu_k. $$What is the total work done by friction as the crate moves a distance $$d up $$the incline?

Accepted Answer

$$W_{fric} = -\mu_k m g d$$

Question 6

A block slides around a square path on a horizontal surface with kinetic friction. After one complete revolution, what is the total work done by the kinetic friction force?

Accepted Answer

The work is negative.

Question 7

A rider of mass $$m is $$pressed against the inner wall of a rotating barrel of radius $$R$$ that spins with angular speed $$\omega. $$The coefficient of static friction between the rider and the wall is $$\mu_s. $$What is the minimum angular speed $$\omega_{min}$$ required so the rider does not fall when the floor is removed?

Accepted Answer

$$\omega_{min} = \sqrt{\dfrac{g}{\mu_s R}}$$

Question 8

A block of mass $$2m is $$connected by a string to a block of mass $$m as $$shown. The system is released from rest. What is the magnitude of the tension $$T in $$the string?

Accepted Answer

$$T = \dfrac{2}{3}mg$$

Question 9

A ball is thrown downward with an initial speed greater than its terminal speed. Which of the following best describes the motion of the ball as it falls?

Accepted Answer

The ball slows down until it reaches terminal speed.

Question 10

A chandelier of mass $$m$$ hangs from the ceiling by a cable. Which statement is correct about the forces acting on the chandelier?

Accepted Answer

The weight and the tension force are equal in magnitude and opposite in direction because the net force must sum to zero by Newton's second law.

Question 11

A block of mass $$m is $$dropped from rest and falls under gravity and air resistance. At terminal speed $$v_t$$, which of the following is true?

Accepted Answer

The net force on the block is zero.

Question 12

A crate of mass $$m is $$pushed at constant speed up a rough incline of angle $$	heta. $$The coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the friction force?

Accepted Answer

$$F_{fric} = \mu_k m g \cos	heta$$

Question 13

A block of mass $$m is $$attached to a spring of force constant $$k$$ and is released from rest at a height $$h$$ above the equilibrium position. Ignoring friction, what is the maximum compression $$x of $$the spring?

Accepted Answer

$$\dfrac{1}{2} m v_i^2$ + mgh = \dfrac{1}{2} k x^2$

Question 14

A block of mass $$m is $$sliding on a horizontal surface with kinetic friction coefficient $$\mu_k. If it $$travels a distance $$d$$ before stopping, what is the initial speed $$v_0 of $$the block?

Accepted Answer

$$v_0$$ = \sqrt{2 \mu_k g d}$$

Question 15

A block of mass $$m is at $$rest on a rough inclined plane of angle $$	heta. $$The coefficient of static friction is $$\mu_s. $$What is the minimum value of $$\mu_s$$ required to prevent the block from sliding down?

Accepted Answer

$$\mu_s = 	an	heta$$

Question 16

A block of mass $$m is $$moving at speed $$v on a $$frictionless surface and collides with a spring of force constant $$k. $$What is the maximum compression $$x_{max} of $$the spring?

Accepted Answer

$$x_{max} = \sqrt{\dfrac{m v^2$}{k}}$$

Question 17

A block of mass $$m is $$pulled at constant speed up a rough incline of angle $$	heta$$ and length $$L. $$The coefficient of kinetic friction is $$\mu_k. $$What is the total work done by all forces on the block?

Accepted Answer

$$W_{total} = 0$$

Question 18

A block of mass $$m is $$attached to a spring and oscillates on a frictionless surface. Which of the following is true about the total mechanical energy of the system?

Accepted Answer

The total mechanical energy remains constant.

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