Q: A person pulls a $$20.0\ \mathrm{kg}$$ box with a rope at an angle of $$30.0^\circ$$ above the horizontal with a force of $$40.0\ \mathrm{N}. $$What is the vertical component of the pulling force?

$$F_{y} = 40.0\ \mathrm{N} \times \sin 30.0^\circ = 20.0\ \mathrm{N}$$

Q: A $$5.0\ \mathrm{kg}$$ block is at rest on a $$30^\circ$$ incline. The coefficient of static friction is $$0.5. $$What is the minimum value of $$\mu_s$$ required to prevent the block from sliding?

$$\mu_s = \tan 30^\circ = 0.577$$

Q: A $$10.0\ \mathrm{kg}$$ box is pulled with a force of $$50.0\ \mathrm{N} at an $$angle of $$30.0^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$0.20$$, what is the net force in the horizontal direction?

$$F_{net} = 50.0\cos 30.0^\circ - 0.20 \times (98.0 - 50.0\sin 30.0^\circ)$$

Question 1

A 20.0-kg box rests on a table. What is the weight of the box?

Accepted Answer

$$196\ \mathrm{N}$$

Question 2

A 10.0-kg box is placed on top of a 20.0-kg box, both at rest on a table. What is the normal force the table exerts on the 20.0-kg box?

Accepted Answer

$$294\ \mathrm{N}$$

Question 3

With the 10.0-kg box on the 20.0-kg box, what is the normal force that the 20.0-kg box exerts on the 10.0-kg box?

Accepted Answer

$$98.0\ \mathrm{N}$$

Question 4

If the stack of boxes is turned upside down so that the 10.0-kg box is on the bottom and the 20.0-kg box is on top, what happens to the normal force between the boxes?

Accepted Answer

The normal force between the boxes would be the same

Question 5

A 14.0-kg lawn mower is pushed at constant speed with a force of $$F = 88.0\ \mathrm{N} at an $$angle of $$45.0^\circ to $$the horizontal. What is the horizontal component of the applied force?

Accepted Answer

$$62.2\ \mathrm{N}$$

Question 6

A 14.0-kg lawn mower is pushed at constant speed with a force of $$F = 88.0\ \mathrm{N} at$$ $$45.0^\circ to $$the horizontal. What is the normal force exerted vertically upward on the mower by the ground?

Accepted Answer

$$199\ \mathrm{N}$$

Question 7

A crate is placed on the bed of a truck. The coefficient of static friction between the crate and the truck is $$\mu_s = 0.75. $$What is the maximum acceleration the truck can have without the crate sliding?

Accepted Answer

$$a_{max} = \mu_s g = 7.35\ \mathrm{m/s^2$}$$

Question 8

A 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord. If the buckets are at rest, what is the tension in the upper cord?

Accepted Answer

$$62.7\ \mathrm{N}$$

Question 9

A block of mass $$m$$ slides down a frictionless incline of angle $$	heta. $$What is the acceleration of the block down the ramp?

Accepted Answer

$$a = g \sin 	heta$$

Question 10

A $$10.0\ \mathrm{kg}$$ box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is $$0.40. $$What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$39.2\ \mathrm{N}$$

Question 11

A $$5.0\ \mathrm{kg}$$ block is sliding down a rough incline of $$30^\circ$$ with a coefficient of kinetic friction $$\mu_k = 0.20. $$What is the net acceleration of the block?

Accepted Answer

$$a = g(\sin 30^\circ - 0.20 \cos 30^\circ)$$

Question 12

Which of the following best describes the normal force acting on an object on an incline of angle $$	heta$$?

Accepted Answer

$$F_N = mg \cos 	heta$$

Question 13

A person pulls a $$20.0\ \mathrm{kg}$$ box with a rope at an angle of $$30.0^\circ$$ above the horizontal with a force of $$40.0\ \mathrm{N}. $$What is the vertical component of the pulling force?

Accepted Answer

$$F_{y} = 40.0\ \mathrm{N} 	imes \sin 30.0^\circ = 20.0\ \mathrm{N}$$

Question 14

A $$10.0\ \mathrm{kg}$$ box is at rest on a horizontal surface. If a horizontal force of $$30.0\ \mathrm{N} is $$applied and the coefficient of kinetic friction is $$0.25$$, what is the acceleration of the box?

Accepted Answer

$$a = \frac{30.0\ \mathrm{N} - (0.25)(98.0\ \mathrm{N})}{10.0\ \mathrm{kg}} = 0.5\ \mathrm{m/s^2$}$$

Question 15

Which of the following statements about friction is correct?

Accepted Answer

The maximum static friction force is $$F_{s, max} = \mu_s F_N$$

Question 16

A $$100\ \mathrm{kg}$$ box is placed on top of a $$20.0\ \mathrm{kg}$$ box, both at rest on a table. What is the normal force the table exerts on the $$20.0\ \mathrm{kg}$$ box?

Accepted Answer

$$1176\ \mathrm{N}$$

Question 17

A block of mass $$m is at $$rest on a rough incline. Which force counteracts the component of gravity perpendicular to the incline?

Accepted Answer

The normal force

Question 18

A $$5.0\ \mathrm{kg}$$ block is at rest on a $$30^\circ$$ incline. The coefficient of static friction is $$0.5. $$What is the minimum value of $$\mu_s$$ required to prevent the block from sliding?

Accepted Answer

$$\mu_s = 	an 30^\circ = 0.577$$

Question 19

A $$10.0\ \mathrm{kg}$$ box is pulled with a force of $$50.0\ \mathrm{N} at an $$angle of $$30.0^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$0.20$$, what is the net force in the horizontal direction?

Accepted Answer

$$F_{net} = 50.0\cos 30.0^\circ - 0.20 	imes (98.0 - 50.0\sin 30.0^\circ)$$

Forces, Normal Force, and Friction: Study Notes for Giancoli Chapter 4

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