Q: If a box is sliding down an inclined plane at angle $$\theta$$ with coefficient of kinetic friction $$\mu_k$$, what is the acceleration $$a of $$the box?

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

Question 1

A car is driving on a wet road and suddenly needs to stop to avoid hitting a deer. If the car's wheels lock and it skids, which type of friction determines the stopping distance, and how does the mass of the car affect the stopping distance?

Accepted Answer

Kinetic friction determines the stopping distance, and the stopping distance does not depend on mass.

Question 2

Which equation correctly defines the friction coefficient $$\mu in $$terms of the friction force $$|f|$$ and the normal force $$N$$?

Accepted Answer

$$\mu = |f| / N$$

Question 3

A box of mass $$m is at $$rest on a horizontal surface. An applied force $$F is $$gradually increased. At what point will the box begin to move?

Accepted Answer

When $$F$$ equals $$\mu_s N$$

Question 4

Why do ABS brakes improve a car's ability to stop quickly compared to locked wheels?

Accepted Answer

Because the friction force from the ground is higher when the wheels are rolling ($$f_s \u003e f_k).$$

Question 5

A box is pushed against a vertical wall with a force $$F. $$What is the minimum force $$F$$ required to keep the box from sliding down, given the coefficient of static friction $$\mu_s$$ and the box's weight $$mg$$?

Accepted Answer

$$F = mg / \mu_s$$

Question 6

A block is placed on an inclined plane. At what angle $$	heta$$ will the block just begin to slide, given the coefficient of static friction $$\mu_s$$?

Accepted Answer

$$	heta = \arctan(\mu_s)$$

Question 7

If a box is sliding down an inclined plane at angle $$	heta$$ with coefficient of kinetic friction $$\mu_k$$, what is the acceleration $$a of $$the box?

Accepted Answer

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

Question 8

Which statement best describes the difference between static and kinetic friction?

Accepted Answer

Static friction acts to prevent motion up to a maximum value; kinetic friction acts when objects are sliding and is usually less than maximum static friction.

Question 9

A person pulls a box of mass $$m$$ along a horizontal surface with a force $$F at an $$angle $$	heta$$ above the horizontal. What is the normal force $$N$$ acting on the box?

Accepted Answer

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

Question 10

Which of the following is true about the friction coefficient $$\mu$$?

Accepted Answer

It is an empirical value that depends on the materials and external conditions.

Question 11

A box is at rest on a surface. An applied force $$F is $$less than the maximum static friction. What is the value of the friction force?

Accepted Answer

It is equal to the applied force $$F.$$

Question 12

When a car turns a corner, what force is responsible for changing its direction?

Accepted Answer

The friction force from the ground acting on the tires.

Question 13

A box is pulled horizontally at constant speed across a rough surface. What is the relationship between the applied force $$F$$ and the kinetic friction force $$f_k$$?

Accepted Answer

$$F = f_k$$

Question 14

If the coefficient of kinetic friction between a box and the floor is $$\mu_k$$, and the normal force is $$N$$, what is the kinetic friction force?

Accepted Answer

$$f_k = \mu_k N$$

Question 15

A truck and a car are both traveling at the same speed and both lock their wheels to stop. Which will have the longer stopping distance, assuming the same coefficient of kinetic friction?

Accepted Answer

Both will have the same stopping distance.

Question 16

A box is sliding on a horizontal surface. If the applied force is suddenly removed, what happens to the box?

Accepted Answer

It decelerates due to kinetic friction until it stops.

Question 17

Which of the following best explains why friction models are not as fundamental as Newton's laws?

Accepted Answer

Friction models are based on empirical coefficients and do not provide an exact description of nature.

Question 18

A person pushes a box of mass $$m$$ along a horizontal surface with a force $$F at an $$angle $$	heta$$ below the horizontal. What is the normal force $$N$$ acting on the box?

Accepted Answer

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

Question 19

A box is at rest on a surface. The maximum static friction force is $$f_{s,	ext{max}} = \mu_s N. If $$the applied force exceeds this value, what happens?

Accepted Answer

The box begins to move and kinetic friction applies.

Module 08: Friction – Physics 211 Study Notes

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