Q: A car of mass 1200 kg is moving in a horizontal circle of radius 50 m at a constant speed of 20 m/s. What is the magnitude of the net force acting on the car?

$$F = m a = m \frac{v^2$}{r} = 1200 \times \frac{20^2$}{50} = 9600\ \mathrm{N}$$

Q: A 5 kg object is suspended by a rope from the ceiling and remains at rest. What is the tension in the rope?

$$T = m g = 5 \times 9.8 = 49\ \mathrm{N}$$

Q: A 2 kg block slides down a ramp inclined at $$30^\circ to $$the horizontal. The coefficient of kinetic friction is 0.2. What is the acceleration of the block down the ramp?

$$a = g \sin \theta - \mu_k g \cos \theta = 9.8 \sin 30^\circ - 0.2 \times 9.8 \cos 30^\circ = 4.9 - 0.2 \times 8.49 = 4.9 - 1.698 = 3.2\ \mathrm{m/s^2$}$$

Q: A 70 kg astronaut weighs 686 N on Earth. What would be the astronaut's weight on the Moon, where $$g_{moon} = 1.62\ \mathrm{m/s^2$}$$?

$$W = m g_{moon} = 70 \times 1.62 = 113.4\ \mathrm{N}$$

Q: A 1.5 kg ball is swung in a vertical circle of radius 2 m at a constant speed. What is the period of revolution if the speed is 4 m/s?

$$T = \frac{2 \pi r}{v} = \frac{2 \pi \times 2}{4} = \pi\ \mathrm{s}$$

Q: A 15 kg box is pulled across a horizontal floor with a force of 60 N at an angle of $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

First, find the normal force: $$N = mg - F \sin \theta = 15 \times 9.8 - 60 \sin 30^\circ = 147 - 30 = 117\ \mathrm{N}. $$Friction force: $$f_k = \mu_k N = 0.3 \times 117 = 35.1\ \mathrm{N}. $$Net force: $$F_{net} = F \cos 30^\circ - f_k = 60 \times 0.866 - 35.1 = 51.96 - 35.1 = 16.86\ \mathrm{N}. $$Acceleration: $$a = F_{net}/m = 16.86/15 = 1.12\ \mathrm{m/s^2$}$$

Q: A 2 kg object is attached to a string and whirled in a horizontal circle of radius 1.5 m at a speed of 3 m/s. What is the tension in the string?

$$T = m \frac{v^2$}{r} = 2 \times \frac{9}{1.5} = 2 \times 6 = 12\ \mathrm{N}$$

Question 1

A 10 kg box is at rest on a horizontal surface. A horizontal force of 30 N is applied to the box, but it does not move. If the coefficient of static friction between the box and the surface is 0.4, which of the following best explains why the box does not move?

Accepted Answer

The applied force is less than the maximum static friction force, so the box remains at rest.

Question 2

A car of mass 1200 kg is moving in a horizontal circle of radius 50 m at a constant speed of 20 m/s. What is the magnitude of the net force acting on the car?

Accepted Answer

$$F = m a = m \frac{v^2$}{r} = 1200 	imes \frac{20^2$}{50} = 9600\ \mathrm{N}$$

Question 3

Which of the following is the correct free-body diagram for a book resting on a table?

Accepted Answer

Two forces: the gravitational force downward and the normal force upward, equal in magnitude and opposite in direction.

Question 4

A 5 kg object is suspended by a rope from the ceiling and remains at rest. What is the tension in the rope?

Accepted Answer

$$T = m g = 5 	imes 9.8 = 49\ \mathrm{N}$$

Question 5

A satellite orbits Earth in a circular orbit of radius $$r. If $$the mass of Earth is $$M$$ and the gravitational constant is $$G$$, what is the speed $$v of $$the satellite?

Accepted Answer

$$v = \sqrt{\frac{G M}{r}}$$

Question 6

A 2 kg block slides down a ramp inclined at $$30^\circ to $$the horizontal. The coefficient of kinetic friction is 0.2. What is the acceleration of the block down the ramp?

Accepted Answer

$$a = g \sin 	heta - \mu_k g \cos 	heta = 9.8 \sin 30^\circ - 0.2 	imes 9.8 \cos 30^\circ = 4.9 - 0.2 	imes 8.49 = 4.9 - 1.698 = 3.2\ \mathrm{m/s^2$}$$

Question 7

Which of the following statements best describes Newton's third law?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 8

A 70 kg astronaut weighs 686 N on Earth. What would be the astronaut's weight on the Moon, where $$g_{moon} = 1.62\ \mathrm{m/s^2$}$$?

Accepted Answer

$$W = m g_{moon} = 70 	imes 1.62 = 113.4\ \mathrm{N}$$

Question 9

A 1.5 kg ball is swung in a vertical circle of radius 2 m at a constant speed. What is the period of revolution if the speed is 4 m/s?

Accepted Answer

$$T = \frac{2 \pi r}{v} = \frac{2 \pi 	imes 2}{4} = \pi\ \mathrm{s}$$

Question 10

A 15 kg box is pulled across a horizontal floor with a force of 60 N at an angle of $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

Accepted Answer

First, find the normal force: $$N = mg - F \sin 	heta = 15 	imes 9.8 - 60 \sin 30^\circ = 147 - 30 = 117\ \mathrm{N}. $$Friction force: $$f_k = \mu_k N = 0.3 	imes 117 = 35.1\ \mathrm{N}. $$Net force: $$F_{net} = F \cos 30^\circ - f_k = 60 	imes 0.866 - 35.1 = 51.96 - 35.1 = 16.86\ \mathrm{N}. $$Acceleration: $$a = F_{net}/m = 16.86/15 = 1.12\ \mathrm{m/s^2$}$$

Question 11

A 2 kg object is attached to a string and whirled in a horizontal circle of radius 1.5 m at a speed of 3 m/s. What is the tension in the string?

Accepted Answer

$$T = m \frac{v^2$}{r} = 2 	imes \frac{9}{1.5} = 2 	imes 6 = 12\ \mathrm{N}$$

Question 12

Which of the following is NOT an action-reaction pair according to Newton's third law?

Accepted Answer

The gravitational force Earth exerts on a book and the normal force the table exerts on the book.

Question 13

A 1000 kg elevator is held at rest by a cable. What is the tension in the cable?

Accepted Answer

$$T = m g = 1000 	imes 9.8 = 9800\ \mathrm{N}$$

Question 14

A 0.5 kg ball is swung in a horizontal circle at the end of a 1 m string. If the string can withstand a maximum tension of 20 N, what is the maximum speed the ball can have before the string breaks?

Accepted Answer

$$T_{max} = m \frac{v^2$}{r} \implies v_{max} = \sqrt{\frac{T_{max} r}{m}} = \sqrt{\frac{20 	imes 1}{0.5}} = \sqrt{40} = 6.32\ \mathrm{m/s}$$

Question 15

A 3 kg object is in free fall near the surface of Earth. What is the net force acting on it, and what is its acceleration?

Accepted Answer

Net force: $$F = m g = 3 	imes 9.8 = 29.4\ \mathrm{N}$$; acceleration: $$a = 9.8\ \mathrm{m/s^2$}$$

Question 16

A 2 kg block is at rest on a horizontal surface. The coefficient of static friction is 0.5. What is the minimum horizontal force required to start moving the block?

Accepted Answer

$$F_{min} = \mu_s m g = 0.5 	imes 2 	imes 9.8 = 9.8\ \mathrm{N}$$

Question 17

A planet has twice the mass of Earth and the same radius. What is the acceleration due to gravity on its surface?

Accepted Answer

$$g' = \frac{G (2M)}{R^2$} = 2g = 19.6\ \mathrm{m/s^2$}$$

Question 18

A 0.2 kg puck slides in a circle of radius 0.5 m on a frictionless horizontal surface at a speed of 2 m/s. What is the required centripetal force?

Accepted Answer

$$F_c = m \frac{v^2$}{r} = 0.2 	imes \frac{4}{0.5} = 0.2 	imes 8 = 1.6\ \mathrm{N}$$

Question 19

A 50 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$N = m (g + a) = 50 	imes (9.8 + 2) = 50 	imes 11.8 = 590\ \mathrm{N}$$

Physics Study Guide: Forces, Newton's Laws, Equilibrium, Friction, and Circular Motion

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