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 1.5 kg mass is suspended from a spring and stretches it by $$\Delta L = 0.10\ \mathrm{m}. $$What is the spring constant $$k$$?

$$k = \frac{mg}{\Delta L} = \frac{1.5 \times 9.8}{0.10} = 147\ \mathrm{N/m}$$

Q: A 5 kg block slides down a frictionless incline of $$30^\circ. $$What is the acceleration of the block?

$$a = g \sin 30^\circ = 9.8 \times 0.5 = 4.9\ \mathrm{m/s^2$}$$

Q: A 1 kg object is hanging from a string inside a car that accelerates to the right. The string makes an angle $$\beta$$ with the vertical. What is the car's acceleration if $$\beta = 45^\circ$$?

$$a = g \tan \beta = 9.8 \tan 45^\circ = 9.8\ \mathrm{m/s^2$}$$

Q: A 20 kg box is pulled across a horizontal floor with a force of 100 N at an angle of $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is 0.2. What is the normal force on the box?

$$n = mg - F \sin 30^\circ = 20 \times 9.8 - 100 \times 0.5 = 196 - 50 = 146\ \mathrm{N}$$

Q: A 3 kg block is pulled by a horizontal force of 15 N across a surface with a kinetic friction coefficient of 0.2. What is the acceleration of the block?

$$a = \frac{F - f_k}{m} = \frac{15 - (0.2 \times 3 \times 9.8)}{3} = \frac{15 - 5.88}{3} = 3.04\ \mathrm{m/s^2$}$$

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

A 2 kg object is pulled by a rope at an angle of $$30^\circ$$ above the horizontal with a tension of 20 N. What is the horizontal component of the force?

Accepted Answer

$$F_x = 20 \cos 30^\circ = 17.32\ \mathrm{N}$$

Question 3

A 1.5 kg mass is suspended from a spring and stretches it by $$\Delta L = 0.10\ \mathrm{m}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{mg}{\Delta L} = \frac{1.5 	imes 9.8}{0.10} = 147\ \mathrm{N/m}$$

Question 4

A car of mass 1000 kg is acted on by a net force of $$F_x = -15000\ \mathrm{N}$$ while moving on a level road. What is its acceleration?

Accepted Answer

$$a = \frac{F_x}{m} = \frac{-15000}{1000} = -15\ \mathrm{m/s^2$}$$

Question 5

A 5 kg block slides down a frictionless incline of $$30^\circ. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin 30^\circ = 9.8 	imes 0.5 = 4.9\ \mathrm{m/s^2$}$$

Question 6

A 1 kg object is hanging from a string inside a car that accelerates to the right. The string makes an angle $$\beta$$ with the vertical. What is the car's acceleration if $$\beta = 45^\circ$$?

Accepted Answer

$$a = g 	an \beta = 9.8 	an 45^\circ = 9.8\ \mathrm{m/s^2$}$$

Question 7

A 20 kg box is pulled across a horizontal floor with a force of 100 N at an angle of $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is 0.2. What is the normal force on the box?

Accepted Answer

$$n = mg - F \sin 30^\circ = 20 	imes 9.8 - 100 	imes 0.5 = 196 - 50 = 146\ \mathrm{N}$$

Question 8

A 1 kg object weighs 9.8 N on Earth and 1.62 N on the Moon. What is the acceleration due to gravity on the Moon?

Accepted Answer

$$g_{moon} = \frac{w}{m} = \frac{1.62}{1} = 1.62\ \mathrm{m/s^2$}$$

Question 9

A block is at rest on a horizontal surface. Which of the following statements is true about the forces acting on the block?

Accepted Answer

The normal force is equal in magnitude and opposite in direction to the weight.

Question 10

A 3 kg block is pulled by a horizontal force of 15 N across a surface with a kinetic friction coefficient of 0.2. What is the acceleration of the block?

Accepted Answer

$$a = \frac{F - f_k}{m} = \frac{15 - (0.2 	imes 3 	imes 9.8)}{3} = \frac{15 - 5.88}{3} = 3.04\ \mathrm{m/s^2$}$$

Question 11

A 5 kg block is connected by a light string to a 2 kg hanging mass over a frictionless pulley. What is the acceleration of the system?

Accepted Answer

$$a = \frac{m_2$ g}{m_1$ + m_2$} = \frac{2 	imes 9.8}{5 + 2} = \frac{19.6}{7} = 2.8\ \mathrm{m/s^2$}$$

Question 12

A block is sliding down a rough incline at constant speed. Which of the following is true?

Accepted Answer

The net force along the incline is zero.

Question 13

A 10 kg object is acted on by two forces: $$\vec{F}_1 = 30\ \mathrm{N}$$ east and $$\vec{F}_2 = 40\ \mathrm{N}$$ north. What is the magnitude of the resultant acceleration?

Accepted Answer

$$a = \frac{\sqrt{30^2$ + 40^2$}}{10} = \frac{50}{10} = 5.0\ \mathrm{m/s^2$}$$

Question 14

A 50 kg skier pushes off horizontally from rest with a force of 100 N. If the coefficient of kinetic friction between the skis and snow is 0.1, what is the skier's acceleration?

Accepted Answer

$$a = \frac{100 - (0.1 	imes 50 	imes 9.8)}{50} = \frac{100 - 49}{50} = 1.02\ \mathrm{m/s^2$}$$

Question 15

A 2 kg block is attached to a spring with $$k = 100\ \mathrm{N/m}. If $$the spring is stretched by 0.05 m, what is the force exerted by the spring?

Accepted Answer

$$F = k \Delta L = 100 	imes 0.05 = 5.0\ \mathrm{N}$$

Question 16

A 10 kg box is at rest on a horizontal surface. If a horizontal force of 20 N is applied and the box does not move, what can you conclude about the coefficient of static friction?

Accepted Answer

$$\mu_s \geq \frac{20}{10 	imes 9.8} = 0.204$$

Newton’s Laws of Motion and Applications: Forces, Equilibrium, and Dynamics

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