Q: A 10 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the minimum horizontal force required to start moving the box?

$$F = 10 \times 9.8 \times 0.4 = 39.2\ \mathrm{N}$$

Q: A 5 kg object is pulled across a horizontal surface with a constant velocity by a horizontal force of 20 N. What is the coefficient of kinetic friction between the object and the surface?

$$\mu_k = \frac{F}{mg} = \frac{20}{5 \times 9.8} = 0.41$$

Q: A 3 kg block slides down a frictionless incline of $$30^\circ. $$What is the acceleration of the block?

$$a = g \sin \theta = 9.8 \times \sin 30^\circ = 4.9\ \mathrm{m/s^2$}$$

Q: A 68.5 kg skater moving at 2.40 m/s comes to rest in 3.52 s due to friction. What is the magnitude of the friction force?

$$F = m a = 68.5 \times \left(\frac{0 - 2.40}{3.52}\right) = -46.7\ \mathrm{N}$$

Q: A 20 kg box is at rest on a ramp inclined at $$25^\circ. $$What is the minimum coefficient of static friction required to keep the box from sliding?

$$\mu_s = \tan 25^\circ = 0.47$$

Q: A 50 kg box is connected by a light string over a frictionless pulley to a 30 kg box on a frictionless $$30^\circ$$ incline. When released, which way will the 50 kg box move and what is the acceleration of the system?

The 50 kg box moves downward with $$a = \frac{50 \times 9.8 - 30 \times 9.8 \sin 30^\circ}{50 + 30} = 4.4\ \mathrm{m/s^2$}$$

Q: A dock worker pulls two boxes connected by a rope on a horizontal floor. The coefficient of static friction is 0.15 and kinetic friction is 0.1. If the worker pulls with 100 N and the total weight is 200 N, what is the friction force acting on the boxes?

$$F_{fr} = \mu_k F_N = 0.1 \times 200 = 20\ \mathrm{N}$$

Question 1

A 10 kg box is at rest on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$F = 10 	imes 9.8 	imes 0.4 = 39.2\ \mathrm{N}$$

Question 2

Which of the following statements about Newton’s Third Law is correct?

Accepted Answer

Action and reaction forces are equal in magnitude and opposite in direction, but act on different objects.

Question 3

A 5 kg object is pulled across a horizontal surface with a constant velocity by a horizontal force of 20 N. What is the coefficient of kinetic friction between the object and the surface?

Accepted Answer

$$\mu_k = \frac{F}{mg} = \frac{20}{5 	imes 9.8} = 0.41$$

Question 4

A 3 kg block slides down a frictionless incline of $$30^\circ. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin 	heta = 9.8 	imes \sin 30^\circ = 4.9\ \mathrm{m/s^2$}$$

Question 5

A 68.5 kg skater moving at 2.40 m/s comes to rest in 3.52 s due to friction. What is the magnitude of the friction force?

Accepted Answer

$$F = m a = 68.5 	imes \left(\frac{0 - 2.40}{3.52}ight) = -46.7\ \mathrm{N}$$

Question 6

A 125 N box is pushed with a force of 75 N at $$30^\circ$$ below the horizontal. The coefficient of static friction is 0.80. What is the normal force on the box?

Accepted Answer

$$N = 125 + 75 \sin 30^\circ = 125 + 37.5 = 162.5\ \mathrm{N}$$

Question 7

A 20 kg box is at rest on a ramp inclined at $$25^\circ. $$What is the minimum coefficient of static friction required to keep the box from sliding?

Accepted Answer

$$\mu_s = 	an 25^\circ = 0.47$$

Question 8

A 50 kg box is connected by a light string over a frictionless pulley to a 30 kg box on a frictionless $$30^\circ$$ incline. When released, which way will the 50 kg box move and what is the acceleration of the system?

Accepted Answer

The 50 kg box moves downward with $$a = \frac{50 	imes 9.8 - 30 	imes 9.8 \sin 30^\circ}{50 + 30} = 4.4\ \mathrm{m/s^2$}$$

Question 9

A dock worker pulls two boxes connected by a rope on a horizontal floor. The coefficient of static friction is 0.15 and kinetic friction is 0.1. If the worker pulls with 100 N and the total weight is 200 N, what is the friction force acting on the boxes?

Accepted Answer

$$F_{fr} = \mu_k F_N = 0.1 	imes 200 = 20\ \mathrm{N}$$

Question 10

A 250 N object is suspended by two cords as shown, one at $$30^\circ$$ and the other at $$45^\circ to $$the ceiling. What is the tension in the cord at $$30^\circ$$?

Accepted Answer

$$T_A = \frac{250 \sin 45^\circ}{\sin(30^\circ + 45^\circ)} = 183\ \mathrm{N}$$

Question 11

A 10 kg box is pulled up a $$20^\circ$$ incline with a force parallel to the incline. The coefficient of kinetic friction is 0.2. What is the net force acting on the box if the pulling force is 50 N?

Accepted Answer

$$F_{net} = 50 - (10 	imes 9.8 \sin 20^\circ + 0.2 	imes 10 	imes 9.8 \cos 20^\circ) = 50 - (33.5 + 18.4) = -1.9\ \mathrm{N}$$

Question 12

A 15 kg box is suspended by a rope. What is the tension in the rope if the box is at rest?

Accepted Answer

$$T = mg = 15 	imes 9.8 = 147\ \mathrm{N}$$

Question 13

A 2 kg object is acted on by a net force of 8 N. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{8}{2} = 4\ \mathrm{m/s^2$}$$

Question 14

A 10 kg box is pulled with a force of 50 N at an angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$F_x = 50 \cos 30^\circ = 43.3\ \mathrm{N}$$

Question 15

A 5 kg box is at rest on a horizontal surface. A force of 15 N is applied horizontally, but the box does not move. If the coefficient of static friction is 0.4, what is the friction force acting on the box?

Accepted Answer

$$F_{fr} = 15\ \mathrm{N}$$

Question 16

A 10 kg box is pulled across a rough floor with a force of 60 N. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

Accepted Answer

$$a = \frac{60 - 0.3 	imes 10 	imes 9.8}{10} = \frac{60 - 29.4}{10} = 3.06\ \mathrm{m/s^2$}$$

Question 17

A 12 kg box is at rest on a horizontal surface. What is the normal force acting on the box?

Accepted Answer

$$N = mg = 12 	imes 9.8 = 117.6\ \mathrm{N}$$

Newton’s Laws of Motion: Statics and Dynamics

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