Q: A flatbed truck carries a 20.0-kg crate. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration the truck can have without the crate sliding?

$$a_{max} = 0.400 \times 9.8\ \mathrm{m/s^2$} = 3.92\ \mathrm{m/s^2$}$$

Q: You push a 33 N block against a vertical wall with a force of 55 N. The coefficients of static and kinetic friction are $$\mu_s = 0.420$$ and $$\mu_k = 0.400. $$Will the block remain at rest?

No, because $$f_{s,max} = \mu_s F_{push} = 0.420 \times 55 = 23.1\ \mathrm{N} \u003c 33\ \mathrm{N}$$, so it will slip.

Q: A 5.0 kg block A is pushed with a 3.0 N force against a 10 kg block B on a frictionless surface. What is the force that block A exerts on block B?

$$F_{A \to B} = \frac{10}{15} \times 3.0 = 2.0\ \mathrm{N}$$

Q: A 200 kg set is suspended by a rope over a pulley. A 100 kg stagehand holds the other end. When the rope is released, what is the acceleration of the stagehand? (Neglect friction and use $$g = 9.8\ \mathrm{m/s^2$})$$

$$a = \frac{(200 - 100)g}{200 + 100} = \frac{100 \times 9.8}{300} = 3.27\ \mathrm{m/s^2$}$$

Q: A block of mass $$m is $$pulled up a rough incline at angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$What is the net force acting on the block parallel to the incline?

$$F_{net} = m g (\sin \theta - \mu_k \cos \theta)$$

Question 1

A 32-kg emperor penguin slides down a 30$$^\circ$$ incline. The coefficient of kinetic friction between the penguin and the incline is 0.350. What is the penguin's acceleration down the incline? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = g(\sin 30^\circ - 0.350 \cos 30^\circ)$$

Question 2

A flatbed truck carries a 20.0-kg crate. The coefficient of static friction between the crate and the bed is 0.400. What is the maximum acceleration the truck can have without the crate sliding?

Accepted Answer

$$a_{max} = 0.400 	imes 9.8\ \mathrm{m/s^2$} = 3.92\ \mathrm{m/s^2$}$$

Question 3

You push a 33 N block against a vertical wall with a force of 55 N. The coefficients of static and kinetic friction are $$\mu_s = 0.420$$ and $$\mu_k = 0.400. $$Will the block remain at rest?

Accepted Answer

No, because $$f_{s,max} = \mu_s F_{push} = 0.420 	imes 55 = 23.1\ \mathrm{N} \u003c 33\ \mathrm{N}$$, so it will slip.

Question 4

If the block in the previous question slips, what is its acceleration down the wall? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = g - \mu_k \frac{F_{push}}{W/g}$$

Question 5

According to Newton’s third law, which statement is correct about the forces between two blocks in contact?

Accepted Answer

The force block A exerts on block B is equal in magnitude and opposite in direction to the force block B exerts on block A.

Question 6

A 5.0 kg block A is pushed with a 3.0 N force against a 10 kg block B on a frictionless surface. What is the force that block A exerts on block B?

Accepted Answer

$$F_{A 	o B} = \frac{10}{15} 	imes 3.0 = 2.0\ \mathrm{N}$$

Question 7

Two blocks, A (1.0 kg) and B (2.0 kg), are connected by a massless string and pulled across a frictionless table. The string breaks if the tension exceeds 6.0 N. What is the maximum force you can apply to block 1 without breaking the string?

Accepted Answer

$$F_{max} = 9.0\ \mathrm{N}$$

Question 8

A box is pulled by a rope with force $$F on a $$frictionless surface. What is the tension in the rope?

Accepted Answer

The tension is equal to the magnitude of the pulling force $$F.$$

Question 9

Two boxes, A and B, are pulled to the right on a frictionless surface and are speeding up. Box A has a larger mass than box B. How do the two tension forces compare?

Accepted Answer

$$T_1$$ \u003e $$T_2$$

Question 10

A mass $$m$$ hangs from a massless string over a massless, frictionless pulley. The other end is attached to a block on a frictionless table. The system accelerates. What is the tension in the string compared to $$mg$$?

Accepted Answer

$$T \u003c mg$$

Question 11

A 200 kg set is suspended by a rope over a pulley. A 100 kg stagehand holds the other end. When the rope is released, what is the acceleration of the stagehand? (Neglect friction and use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{(200 - 100)g}{200 + 100} = \frac{100 	imes 9.8}{300} = 3.27\ \mathrm{m/s^2$}$$

Question 12

Which of the following is true for a massless rope passing over a massless, frictionless pulley?

Accepted Answer

The tension is the same on both sides of the pulley.

Question 13

A block of mass $$m is $$pulled up a rough incline at angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$What is the net force acting on the block parallel to the incline?

Accepted Answer

$$F_{net} = m g (\sin 	heta - \mu_k \cos 	heta)$$

Question 14

If you pull on one end of a massless rope with force $$F$$, what force does the other end of the rope exert on the object it is attached to?

Accepted Answer

A force of magnitude $$F.$$

Question 15

A 10 kg block is connected by a massless rope over a frictionless pulley to a 5 kg block. If the system is released from rest, what is the acceleration of the blocks? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{(10 - 5)g}{10 + 5} = 3.27\ \mathrm{m/s^2$}$$

Question 16

Which of the following best describes the action/reaction pair when a box is pulled by a rope?

Accepted Answer

The force the rope exerts on the box and the force the box exerts on the rope.

Applying Newton's Laws: Friction, Interacting Objects, Ropes, and Pulleys

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