Q: A block of mass $$m is on an $$incline at angle $$\theta to $$the horizontal. If the coefficient of kinetic friction is $$\mu_k$$, what is the acceleration of the block down the incline?

$$a = g (\sin \theta - \mu_k \cos \theta)$$

Q: A block is being pulled along a floor by a constant force $$F at an $$angle $$\theta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$What is the expression for the frictional force?

$$f_k = \mu_k (mg - F \sin \theta)$$

Q: Two blocks of masses $$m_1$$ and $$m_2$$ are connected by a rope and slide down an incline with angle $$\theta$$ and kinetic friction coefficient $$\mu_k. $$What is the acceleration of the system?

$$a = g (\sin \theta - \mu_k \cos \theta)$$

Q: A block is pulled at constant speed up a rough incline by a force parallel to the incline. If the incline angle is $$\theta$$ and the coefficient of kinetic friction is $$\mu_k$$, what is the magnitude of the pulling force?

$$F = mg (\sin \theta + \mu_k \cos \theta)$$

Question 1

A hockey puck of mass $$m$$ slides in a circle of radius $$r on a $$frictionless table while attached to a string. If the puck moves with constant speed $$v$$, what is the magnitude of the acceleration?

Accepted Answer

$$a = \dfrac{v^2$}{r}$$

Question 2

A block of mass $$m is on an $$incline at angle $$	heta to $$the horizontal. If the coefficient of kinetic friction is $$\mu_k$$, what is the acceleration of the block down the incline?

Accepted Answer

$$a = g (\sin 	heta - \mu_k \cos 	heta)$$

Question 3

Which of the following best describes Newton's Second Law in component form for an object acted on by forces $$F_{x,1}$$, $$F_{x,2}$$, ..., $$F_{x,n}$$ along the $$x-$$axis?

Accepted Answer

$$\sum_{i=1}^n F_{x,i} = m a_x$$

Question 4

A block is being pulled along a floor by a constant force $$F at an $$angle $$	heta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$What is the expression for the frictional force?

Accepted Answer

$$f_k = \mu_k (mg - F \sin 	heta)$$

Question 5

A rope pulls a crate of mass $$m$$ with tension $$T$$ across a horizontal surface with kinetic friction coefficient $$\mu_k. If $$the crate moves at constant velocity, what is the value of $$T$$?

Accepted Answer

$$T = \mu_k m g$$

Question 6

A block of mass $$m is at $$rest on a horizontal surface. A horizontal force $$F is $$applied. If $$F is $$less than the maximum static friction force, what happens?

Accepted Answer

The block does not move.

Question 7

A hockey puck slides on ice and slows down due to kinetic friction. If the coefficient of kinetic friction is $$\mu_k$$ and the puck's initial speed is $$v_0$$, what is the distance $$d it $$travels before stopping?

Accepted Answer

$$d = \dfrac{v_0$^2}{2 \mu_k g}$$

Question 8

A block of mass $$m is $$attached to a rope and pulled vertically upward at constant speed. What is the tension in the rope?

Accepted Answer

$$T = mg$$

Question 9

A car of mass $$m$$ moves at constant speed $$v$$ around a flat circular track of radius $$R. $$What is the minimum coefficient of static friction $$\mu_s$$ required to prevent slipping?

Accepted Answer

$$\mu_s = \dfrac{v^2$}{g R}$$

Question 10

Two blocks of masses $$m_1$$ and $$m_2$$ are connected by a rope and slide down an incline with angle $$	heta$$ and kinetic friction coefficient $$\mu_k. $$What is the acceleration of the system?

Accepted Answer

$$a = g (\sin 	heta - \mu_k \cos 	heta)$$

Question 11

A block is sliding down a rough incline at constant velocity. Which statement is true?

Accepted Answer

The net force on the block is zero.

Question 12

A block of mass $$m is $$pulled by a force $$F at an $$angle $$	heta$$ above the horizontal across a rough surface. The normal force $$N is $$given by:

Accepted Answer

$$N = mg - F \sin 	heta$$

Question 13

A block is at rest on a horizontal surface. The maximum static friction force is $$f_{s,	ext{max}} = \mu_s N. If a $$force $$F is $$applied and $$F \u003e f_{s,	ext{max}}$$, what happens?

Accepted Answer

The block begins to move.

Question 14

A block of mass $$m is $$sliding on a horizontal surface with kinetic friction coefficient $$\mu_k. $$What is the acceleration of the block?

Accepted Answer

$$a = -\mu_k g$$

Question 15

A block of mass $$m is $$attached to a string and spun in a horizontal circle of radius $$R at $$constant speed $$v. $$What is the tension in the string?

Accepted Answer

$$T = m \dfrac{v^2$}{R}$$

Question 16

A block is pulled at constant speed up a rough incline by a force parallel to the incline. If the incline angle is $$	heta$$ and the coefficient of kinetic friction is $$\mu_k$$, what is the magnitude of the pulling force?

Accepted Answer

$$F = mg (\sin 	heta + \mu_k \cos 	heta)$$

Question 17

A block of mass $$m is $$sliding down a frictionless incline of angle $$	heta. $$What is its acceleration?

Accepted Answer

$$a = g \sin 	heta$$

Question 18

A block is sliding on a horizontal surface with kinetic friction. If the block's mass is doubled, what happens to the acceleration due to friction?

Accepted Answer

It remains the same.

Question 19

A block of mass $$m is $$pulled by a force $$F at $$constant velocity across a horizontal surface with kinetic friction coefficient $$\mu_k. $$What is the value of $$F$$?

Accepted Answer

$$F = \mu_k m g$$

Question 20

A block is sliding down an incline with angle $$	heta$$ and coefficient of kinetic friction $$\mu_k. If$$ $$\mu_k$$ increases, what happens to the acceleration of the block?

Accepted Answer

It decreases.

Study Guide: Forces, Friction, and Drag in Newtonian Mechanics

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