Q: A 2 kg block is pushed along a frictionless horizontal surface with a constant force of 10 N. What is the acceleration of the block?

$$a = \frac{10\ \text{N}}{2\ \text{kg}} = 5\ \text{m/s}^2$$

Q: A ball is thrown horizontally from the top of a 20 m high building. Neglecting air resistance, what is the speed of the ball just before it hits the ground?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 20} \approx 19.8\ \text{m/s}$$

Q: A 5 kg object is suspended by a rope. What is the tension in the rope if the object is at rest?

$$T = mg = 5 \times 9.8 = 49\ \text{N}$$

Q: A 10 kg box is pulled across a rough floor with a force of 50 N. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

$$a = \frac{F - f_k}{m} = \frac{50 - (0.3 \times 10 \times 9.8)}{10} = \frac{50 - 29.4}{10} = 2.06\ \text{m/s}^2$$

Q: A car of mass 1200 kg rounds a banked curve of radius 50 m at a speed of 20 m/s. If the curve is banked at an angle $$\theta$$ such that no friction is required, what is $$\theta$$?

$$\tan\theta = \frac{v^2$}{rg}$$, so $$\theta = \arctan\left(\frac{20^2$}{50 \times 9.8}\right) \approx 16.5^\circ$$

Q: A 3 kg object is pushed 4 m across a floor by a force of 10 N at an angle of $$30^\circ to $$the horizontal. What is the work done by the force?

$$W = Fd\cos\theta = 10 \times 4 \times \cos 30^\circ = 40 \times 0.866 = 34.64\ \text{J}$$

Q: A spring with constant $$k = 200\ \text{N/m} is $$compressed by 0.5 m. What is the potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.5)^2$ = 25\ \text{J}$$

Q: A 2 kg object is released from rest at the top of a 5 m high hill. Neglecting friction, what is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} \approx 9.9\ \text{m/s}$$

Q: A 1 kg block is attached to a horizontal spring ($$k = 100\ \text{N/m}) $$and compressed by 0.2 m. If the block is released, what is its speed as it passes through equilibrium, assuming no friction?

$$v = \sqrt{\frac{kx^2$}{m}} = \sqrt{\frac{100 \times (0.2)^2$}{1}} = \sqrt{4} = 2\ \text{m/s}$$

Question 1

A 2 kg block is pushed along a frictionless horizontal surface with a constant force of 10 N. What is the acceleration of the block?

Accepted Answer

$$a = \frac{10\ 	ext{N}}{2\ 	ext{kg}} = 5\ 	ext{m/s}^2$$

Question 2

A ball is thrown horizontally from the top of a 20 m high building. Neglecting air resistance, what is the speed of the ball just before it hits the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} \approx 19.8\ 	ext{m/s}$$

Question 3

The acceleration due to gravity $$g at $$the surface of a planet is given by which formula?

Accepted Answer

$$g = \frac{GM}{R^2$}$$

Question 4

A 5 kg object is suspended by a rope. What is the tension in the rope if the object is at rest?

Accepted Answer

$$T = mg = 5 	imes 9.8 = 49\ 	ext{N}$$

Question 5

A 10 kg box is pulled across a rough floor with a force of 50 N. The coefficient of kinetic friction is 0.3. What is the acceleration of the box?

Accepted Answer

$$a = \frac{F - f_k}{m} = \frac{50 - (0.3 	imes 10 	imes 9.8)}{10} = \frac{50 - 29.4}{10} = 2.06\ 	ext{m/s}^2$$

Question 6

A car of mass 1200 kg rounds a banked curve of radius 50 m at a speed of 20 m/s. If the curve is banked at an angle $$	heta$$ such that no friction is required, what is $$	heta$$?

Accepted Answer

$$	an	heta = \frac{v^2$}{rg}$$, so $$	heta = \arctan\left(\frac{20^2$}{50 	imes 9.8}ight) \approx 16.5^\circ$$

Question 7

A skydiver of mass 80 kg falls through the air and eventually reaches terminal speed. Which statement best describes terminal speed?

Accepted Answer

Terminal speed is reached when the upward resistive force equals the downward gravitational force, so $$mg = F_{	ext{drag}}$$

Question 8

The mathematical expression for terminal speed $$v_t$$ for a falling object with drag force $$F_{	ext{drag}} = bv is$$:

Accepted Answer

$$v_t = \frac{mg}{b}$$

Question 9

Which equation defines the work $$W$$ done by a constant force $$\vec{F}$$ acting over a displacement $$\vec{d}$$?

Accepted Answer

$$W = \vec{F} \cdot \vec{d}$$

Question 10

A 3 kg object is pushed 4 m across a floor by a force of 10 N at an angle of $$30^\circ to $$the horizontal. What is the work done by the force?

Accepted Answer

$$W = Fd\cos	heta = 10 	imes 4 	imes \cos 30^\circ = 40 	imes 0.866 = 34.64\ 	ext{J}$$

Question 11

A spring with constant $$k = 200\ 	ext{N/m} is $$compressed by 0.5 m. What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.5)^2$ = 25\ 	ext{J}$$

Question 12

A 2 kg object is released from rest at the top of a 5 m high hill. Neglecting friction, what is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9\ 	ext{m/s}$$

Question 13

A 1 kg block is attached to a horizontal spring ($$k = 100\ 	ext{N/m}) $$and compressed by 0.2 m. If the block is released, what is its speed as it passes through equilibrium, assuming no friction?

Accepted Answer

$$v = \sqrt{\frac{kx^2$}{m}} = \sqrt{\frac{100 	imes (0.2)^2$}{1}} = \sqrt{4} = 2\ 	ext{m/s}$$

Question 14

A 4 kg object is dropped from a height of 10 m. If air resistance does 20 J of work on the object, what is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{\frac{2(mgh - W_{	ext{air}})}{m}} = \sqrt{\frac{2(4 	imes 9.8 	imes 10 - 20)}{4}} = \sqrt{\frac{2(392 - 20)}{4}} = \sqrt{\frac{744}{4}} = \sqrt{186} \approx 13.6\ 	ext{m/s}$$

Question 15

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Speed is a scalar quantity (magnitude only), while velocity is a vector quantity (magnitude and direction).

Question 16

A planet has mass $$M$$ and radius $$R. If $$its density is $$\rho$$, which equation relates $$M$$, $$R$$, and $$\rho$$?

Accepted Answer

$$M = \frac{4}{3}\pi R^3$ \rho$$

Question 17

Two blocks, masses $$m_1 = 2$$\ 	ext{kg}$$ and m_2$ = 3\ 	ext{kg}$$, are connected by a rope and pulled horizontally with a force of 20 N. If friction is negligible, what is the acceleration of the system?

Accepted Answer

$$a = \frac{F}{m_1$ + m_2$} = \frac{20}{5} = 4\ 	ext{m/s}^2$$

Question 18

A 1 kg object moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = \frac{mv^2$}{r} = \frac{1 	imes 16}{2} = 8\ 	ext{N}$$

Exam 2 Study Guide: Newton’s Laws, Gravitation, Circular Motion, Work, and Energy

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