Q: A 2 kg block is attached to a rope and swung in a horizontal circle of radius 1.5 m at a constant speed of 4 m/s. What is the tension in the rope?

$$T = m a_c = m \frac{v^2$}{r} = 2 \times \frac{4^2$}{1.5} = 2 \times \frac{16}{1.5} = 2 \times 10.67 = 21.33\ \mathrm{N}$$

Q: A 5 kg box rests on a frictionless inclined plane that makes a $$30^\circ$$ angle with the horizontal. What is the component of the gravitational force acting parallel to the incline?

$$F_{g,\parallel} = m g \sin \theta = 5 \times 9.8 \times \sin 30^\circ = 5 \times 9.8 \times 0.5 = 24.5\ \mathrm{N}$$

Q: A 1.5 kg object is dropped from rest from a height of 10 m. Ignoring air resistance, what is its speed just before it hits the ground?

$$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 10} = \sqrt{196} = 14\ \mathrm{m/s}$$

Q: A 3 kg object is moving at 6 m/s. What is its kinetic energy?

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} \times 3 \times 6^2$ = 1.5 \times 36 = 54\ \mathrm{J}$$

Q: A spring with a force constant $$k = 200\ \mathrm{N/m} is $$compressed by 0.1 m. What is the work done by the spring during this compression?

$$W = \frac{1}{2} k x^2$ = 0.5 \times 200 \times (0.1)^2$ = 0.5 \times 200 \times 0.01 = 1\ \mathrm{J}$$

Q: A 2 kg object slides down a frictionless incline from a height of 5 m. What is its speed at the bottom?

$$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 5} = \sqrt{98} = 9.9\ \mathrm{m/s}$$

Question 1

A 2 kg block is attached to a rope and swung in a horizontal circle of radius 1.5 m at a constant speed of 4 m/s. What is the tension in the rope?

Accepted Answer

$$T = m a_c = m \frac{v^2$}{r} = 2 	imes \frac{4^2$}{1.5} = 2 	imes \frac{16}{1.5} = 2 	imes 10.67 = 21.33\ \mathrm{N}$$

Question 2

Which of the following best describes Newton’s Third Law?

Accepted Answer

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

Question 3

A 5 kg box rests on a frictionless inclined plane that makes a $$30^\circ$$ angle with the horizontal. What is the component of the gravitational force acting parallel to the incline?

Accepted Answer

$$F_{g,\parallel} = m g \sin 	heta = 5 	imes 9.8 	imes \sin 30^\circ = 5 	imes 9.8 	imes 0.5 = 24.5\ \mathrm{N}$$

Question 4

A 1.5 kg object is dropped from rest from a height of 10 m. Ignoring air resistance, what is its speed just before it hits the ground?

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 10} = \sqrt{196} = 14\ \mathrm{m/s}$$

Question 5

Which of the following statements correctly distinguishes between mass and weight?

Accepted Answer

Mass is a measure of the amount of matter in an object, while weight is the force of gravity acting on that mass.

Question 6

A 3 kg object is moving at 6 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 3 	imes 6^2$ = 1.5 	imes 36 = 54\ \mathrm{J}$$

Question 7

A 10 kg crate is pulled across a rough floor at constant speed by a force of 50 N acting at an angle of $$30^\circ$$ above the horizontal. What is the frictional force acting on the crate?

Accepted Answer

Since the crate moves at constant speed, friction balances the horizontal component of the applied force: $$f = F \cos 	heta = 50 \cos 30^\circ = 50 	imes 0.866 = 43.3\ \mathrm{N}$$

Question 8

A spring with a force constant $$k = 200\ \mathrm{N/m} is $$compressed by 0.1 m. What is the work done by the spring during this compression?

Accepted Answer

$$W = \frac{1}{2} k x^2$ = 0.5 	imes 200 	imes (0.1)^2$ = 0.5 	imes 200 	imes 0.01 = 1\ \mathrm{J}$$

Question 9

A 2 kg object slides down a frictionless incline from a height of 5 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 5} = \sqrt{98} = 9.9\ \mathrm{m/s}$$

Question 10

A 4 kg object is acted on by a net force of 12 N. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{12}{4} = 3\ \mathrm{m/s^2$}$$

Question 11

A 1.2 kg ball is thrown vertically upward with an initial speed of 8 m/s. What is the maximum height it reaches? (Ignore air resistance.)

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{8^2$}{2 	imes 9.8} = \frac{64}{19.6} = 3.27\ \mathrm{m}$$

Question 12

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 maximum horizontal force that can be applied before the box starts to move?

Accepted Answer

$$F_{max} = \mu_s N = 0.4 	imes 10 	imes 9.8 = 0.4 	imes 98 = 39.2\ \mathrm{N}$$

Question 13

A 2 kg object is pushed up a 3 m long frictionless ramp inclined at $$20^\circ to $$the horizontal. What is the minimum work required to move the object to the top?

Accepted Answer

The minimum work equals the gain in gravitational potential energy: $$W = m g h = 2 	imes 9.8 	imes (3 \sin 20^\circ) = 2 	imes 9.8 	imes 1.026 = 20.1\ \mathrm{J}$$

Question 14

A 0.5 kg ball is attached to a string and swung in a vertical circle of radius 2 m. At the lowest point, the ball's speed is 6 m/s. What is the tension in the string at this point?

Accepted Answer

$$T = m g + m \frac{v^2$}{r} = 0.5 	imes 9.8 + 0.5 	imes \frac{36}{2} = 4.9 + 9 = 13.9\ \mathrm{N}$$

Question 15

A 1.5 kg block slides across a rough surface and comes to rest after 4 m. If the coefficient of kinetic friction is 0.3, what was the block's initial speed?

Accepted Answer

Work done by friction: $$W = -f_k d = -\mu_k m g d. $$Set $$\Delta KE = W$$: $$\frac{1}{2} m v^2$ = \mu_k m g d \implies v = \sqrt{2 \mu_k g d} = \sqrt{2 	imes 0.3 	imes 9.8 	imes 4} = \sqrt{23.52} = 4.85\ \mathrm{m/s}$$

Question 16

A 2 kg object is in equilibrium on a frictionless table, acted on by two forces: $$F_1 = 10$$\ \mathrm{N}$$ east and F_2$ at an angle $$	heta$$ north of west. What must be the magnitude and direction of F_2$ for equilibrium?

Accepted Answer

$$F_2 = 10$$\ \mathrm{N}$$, west

Question 17

A 3 kg object is pulled by a force of 15 N at an angle of $$60^\circ$$ above the horizontal on a frictionless surface. What is the horizontal acceleration of the object?

Accepted Answer

Horizontal force: $$F_x = 15 \cos 60^\circ = 15 	imes 0.5 = 7.5\ \mathrm{N}$$. $$a = \frac{F_x}{m} = \frac{7.5}{3} = 2.5\ \mathrm{m/s^2$}$$

Question 18

A 2 kg block is at rest on a 25$$^\circ$$ incline. What is the normal force acting on the block?

Accepted Answer

$$N = m g \cos 	heta = 2 	imes 9.8 	imes \cos 25^\circ = 2 	imes 9.8 	imes 0.906 = 17.76\ \mathrm{N}$$

Question 19

A 1 kg object is thrown horizontally from a 20 m high cliff. How far from the base of the cliff does it land if its initial speed is 5 m/s? (Ignore air resistance.)

Accepted Answer

Time to fall: $$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} = 2.02\ \mathrm{s}. $$Horizontal distance: $$d = v t = 5 	imes 2.02 = 10.1\ \mathrm{m}$$

Physics Study Guide: Newton's Laws, Circular Motion, Work, and Energy (Chapters 5–8)

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