Q: A block of mass $$m$$ slides down an inclined plane of angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

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

Q: In a system with a block on an incline connected to a hanging mass, what is the criterion for the block on the incline to pull the hanging mass up?

$$m_1g\sin\theta + \mu m_1g\cos\theta \u003e m_2g$$

Question 1

A 10 kg block is suspended as shown in the diagram by two strings, with $$T_1 at a$$ $$45^\circ$$ angle to the horizontal and $$T_2$$ horizontal. What is the magnitude of $$T_1$$? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$T_1 = 69.3$$\ \mathrm{N}$$

Question 2

A block of mass $$m_1$$ sits on a slab of mass $$m_2 on a $$frictionless surface. The coefficient of friction between the block and the slab is $$\mu. $$What is the maximum acceleration the system can have before the block slips relative to the slab?

Accepted Answer

$$a_{max} = \mu g$$

Question 3

A crate with mass $$50.0\ \mathrm{kg} is at $$rest on a rough horizontal surface with $$\mu_s = 0.40$$ and $$\mu_k = 0.20. If a $$man pushes with a horizontal force of $$150\ \mathrm{N}$$, what is the force of friction on the crate?

Accepted Answer

$$f = 150\ \mathrm{N}$$

Question 4

Which of the following correctly describes the relationship between the coefficients of friction for a given pair of surfaces?

Accepted Answer

$$\mu_s \u003e \mu_k \u003e \mu_r$$

Question 5

A sled of mass $$80\ \mathrm{kg} is $$pulled with a force of $$170\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. The coefficients of friction are $$\mu_s = 0.4$$ and $$\mu_k = 0.2. $$What is the acceleration of the sled? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = 0.44\ \mathrm{m/s^2$}$$

Question 6

A block is on the verge of slipping on a horizontal surface. Which equation correctly gives the maximum static friction force?

Accepted Answer

$$f_{s,max} = \mu_s N$$

Question 7

A block is pulled across a horizontal surface at constant speed. Which of the following statements is true about the friction force?

Accepted Answer

The friction force is equal to the applied force.

Question 8

A block of mass $$m$$ slides down an inclined plane of angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

Accepted Answer

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

Question 9

In a system where a block $$m_1 on a $$table is connected by a string over a pulley to a hanging mass $$m_2$$, which equation correctly describes the forces on the hanging mass?

Accepted Answer

$$m_2g - T = m_2a$$

Question 10

A block is at rest on a horizontal surface. Which of the following is true about the static friction force acting on it?

Accepted Answer

$$f_s \u003c \mu_s N$$

Question 11

A block is being pulled to the right with a force $$T on a $$rough surface. Which forces should be included in the free-body diagram for the block?

Accepted Answer

Tension $$T$$, normal force $$n$$, weight $$w$$, and static friction $$f_s$$

Question 12

A block is pulled at constant speed across a surface. Which coefficient is relevant for calculating the friction force?

Accepted Answer

Coefficient of kinetic friction $$\mu_k$$

Question 13

A block is pushed and is speeding up. Which of the following correctly ranks the friction forces in the scenarios: (a) at rest, (b) on the verge of slipping, (c) speeding up, (d) constant speed, (e) slowing down?

Accepted Answer

$$f_c \u003e f_d \u003e f_e \u003e f_b \u003e f_a$$

Question 14

A sled is pulled with a force $$F at$$ $$30^\circ$$ above the horizontal in case (a), and pushed with the same force at $$30^\circ$$ below the horizontal in case (b). Which statement is true about the friction force in both cases?

Accepted Answer

$$f_a \u003c f_b$$

Question 15

A block of mass $$m is $$pulled across a rough surface with a force $$F at an $$angle $$	heta$$ above the horizontal. What is the normal force $$N$$ acting on the block?

Accepted Answer

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

Question 16

A block of mass $$m is $$sliding down an incline of angle $$	heta$$ with friction. What is the expression for the normal force $$N$$?

Accepted Answer

$$N = mg\cos	heta$$

Question 17

In a system with a block on an incline connected to a hanging mass, what is the criterion for the block on the incline to pull the hanging mass up?

Accepted Answer

$$m_1g\sin	heta + \mu m_1g\cos	heta \u003e m_2g$$

Question 18

Which of the following is NOT a force that should be included in the free-body diagram for a massless ring at the intersection of three strings?

Accepted Answer

Force of gravity on the block (if the ring is massless)

Applying Newton’s Laws: Friction, Connected Objects, and Inclined Planes

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