Q: A block of mass $$m is $$being pulled up a rough incline at constant speed. The incline makes an angle $$\theta$$ with the horizontal, and the coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the pulling force $$F$$ parallel to the incline?

$$F = m g (\sin \theta + \mu_k \cos \theta)$$

Q: A block of mass $$m is $$sliding down a ramp of angle $$\theta$$ with kinetic friction coefficient $$\mu_k. $$What is the acceleration of the block?

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

Question 1

A block of mass $$m is at $$rest on a horizontal surface. The coefficient of static friction between the block and the surface is $$\mu_s. $$What is the maximum horizontal force that can be applied to the block before it starts to move?

Accepted Answer

$$\mu_s m g$$

Question 2

A 10 kg box is pulled across a horizontal floor at constant speed. The coefficient of kinetic friction between the box and the floor is $$0.3. $$What is the magnitude of the frictional force acting on the box?

Accepted Answer

$$30\ \mathrm{N}$$

Question 3

Which of the following best describes the direction of the friction force acting on a moving object?

Accepted Answer

Opposite to the direction of motion

Question 4

A block is at rest on a rough surface. A horizontal force $$F is $$applied, but the block does not move. Which equation correctly describes the static friction force $$f_s$$?

Accepted Answer

$$f_s = F$$

Question 5

A car is moving at a constant speed on a flat road. Which force is responsible for propelling the car forward?

Accepted Answer

The friction force of the ground on the tires

Question 6

A block slides down a ramp at constant speed. The coefficient of kinetic friction between the block and the ramp is $$\mu_k. If $$the ramp makes an angle $$	heta$$ with the horizontal, what is the relationship between $$\mu_k$$ and $$	heta$$?

Accepted Answer

$$\mu_k = 	an 	heta$$

Question 7

A skydiver of mass $$m$$ falls through the air and eventually reaches terminal velocity. If the air resistance at high speed is given by $$f = D v^2$, what is the expression for the terminal velocity v_t$?

Accepted Answer

$$v_t = \sqrt{\frac{mg}{D}}$$

Question 8

Which of the following statements about static and kinetic friction is correct?

Accepted Answer

The maximum static friction is usually greater than the kinetic friction for the same surfaces.

Question 9

A block of mass $$m is $$being pulled up a rough incline at constant speed. The incline makes an angle $$	heta$$ with the horizontal, and the coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the pulling force $$F$$ parallel to the incline?

Accepted Answer

$$F = m g (\sin 	heta + \mu_k \cos 	heta)$$

Question 10

A 5 kg block is at rest on a horizontal surface. The coefficient of static friction is $$0.4. $$What is the minimum force required to start moving the block?

Accepted Answer

$$19.6\ \mathrm{N}$$

Question 11

A block is sliding at constant speed on a horizontal surface. Which equation correctly gives the kinetic friction force $$f_k$$?

Accepted Answer

$$f_k = \mu_k n$$

Question 12

A 2 kg object falls through a fluid where the resistive force is proportional to velocity: $$f = k v. If$$ $$k = 4\ \mathrm{kg/s}$$, what is the terminal velocity?

Accepted Answer

$$v_t = 4.9\ \mathrm{m/s}$$

Question 13

Which of the following best explains why a person is able to walk forward?

Accepted Answer

The ground exerts a forward friction force on the person's feet.

Question 14

A block is at rest on a horizontal surface. An increasing horizontal force is applied until the block just begins to move. Which statement is true at the instant the block starts to move?

Accepted Answer

$$f_s = \mu_s n$$

Question 15

A 3 kg block is pulled with a force of 20 N on a horizontal surface. The coefficient of kinetic friction is $$0.2. $$What is the acceleration of the block?

Accepted Answer

$$4.7\ \mathrm{m/s^2$}$$

Question 16

A block is being pulled at constant speed across a horizontal surface. If the coefficient of kinetic friction is doubled, what happens to the required pulling force?

Accepted Answer

It doubles

Question 17

Which of the following is true about the coefficients of friction for different material pairs?

Accepted Answer

The coefficient of static friction is generally higher than the coefficient of kinetic friction for the same materials.

Question 18

A block of mass $$m is $$sliding down a ramp of angle $$	heta$$ with kinetic friction coefficient $$\mu_k. $$What is the acceleration of the block?

Accepted Answer

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

Friction Forces and Applications in Classical Mechanics

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