Q: A 10 kg box rests on a horizontal surface. If 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?

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

Q: A 5 kg object is suspended by a rope over a frictionless pulley and connected to a 3 kg object on a horizontal table (ignore friction). What is the acceleration of the system?

$$a = \frac{m_1$ g}{m_1$ + m_2$} = \frac{5 \times 9.8}{5 + 3} = 6.125\ \mathrm{m/s^2$}$$

Q: A 2 kg mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}. $$The spring is compressed by 0.1 m and then released from rest. What is the speed of the mass as it passes through the equilibrium position (ignore friction)?

$$v = \sqrt{\frac{k x^2$}{m}} = \sqrt{\frac{200 \times 0.01}{2}} = 1\ \mathrm{m/s}$$

Q: A car of mass 1000 kg rounds a curve of radius 50 m at a speed of 10 m/s. What is the magnitude of the required centripetal force?

$$F_c = m a_c = m \frac{v^2$}{r} = 1000 \times \frac{100}{50} = 2000\ \mathrm{N}$$

Q: A 60 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

$$N = m (g + a) = 60 \times (9.8 + 2) = 708\ \mathrm{N}$$

Q: A force $$F is $$applied to a 4 kg block, causing it to move at constant velocity across a horizontal surface. If the coefficient of kinetic friction is 0.25, what is the magnitude of $$F$$?

$$F = \mu_k N = 0.25 \times 4 \times 9.8 = 9.8\ \mathrm{N}$$

Q: A 2 kg object is dropped from a height of 5 m. Ignoring air resistance, what is its speed just before hitting the ground?

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

Q: A force vs. position graph for an object shows a constant force of 5 N applied over a distance of 4 m. What is the work done on the object?

$$W = F d = 5 \times 4 = 20\ \mathrm{J}$$

Q: A 100 W light bulb is left on for 2 hours. How much energy does it consume in joules?

$$E = P t = 100 \times (2 \times 3600) = 720,000\ \mathrm{J}$$

Question 1

A 10 kg box rests on a horizontal surface. If 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

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

Question 2

A 5 kg object is suspended by a rope over a frictionless pulley and connected to a 3 kg object on a horizontal table (ignore friction). What is the acceleration of the system?

Accepted Answer

$$a = \frac{m_1$ g}{m_1$ + m_2$} = \frac{5 	imes 9.8}{5 + 3} = 6.125\ \mathrm{m/s^2$}$$

Question 3

A 2 kg mass is attached to a spring with spring constant $$k = 200\ \mathrm{N/m}. $$The spring is compressed by 0.1 m and then released from rest. What is the speed of the mass as it passes through the equilibrium position (ignore friction)?

Accepted Answer

$$v = \sqrt{\frac{k x^2$}{m}} = \sqrt{\frac{200 	imes 0.01}{2}} = 1\ \mathrm{m/s}$$

Question 4

A car of mass 1000 kg rounds a curve of radius 50 m at a speed of 10 m/s. What is the magnitude of the required centripetal force?

Accepted Answer

$$F_c = m a_c = m \frac{v^2$}{r} = 1000 	imes \frac{100}{50} = 2000\ \mathrm{N}$$

Question 5

A 60 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$N = m (g + a) = 60 	imes (9.8 + 2) = 708\ \mathrm{N}$$

Question 6

A force $$F is $$applied to a 4 kg block, causing it to move at constant velocity across a horizontal surface. If the coefficient of kinetic friction is 0.25, what is the magnitude of $$F$$?

Accepted Answer

$$F = \mu_k N = 0.25 	imes 4 	imes 9.8 = 9.8\ \mathrm{N}$$

Question 7

A 2 kg object is dropped from a height of 5 m. Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

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

Question 8

A force vs. position graph for an object shows a constant force of 5 N applied over a distance of 4 m. What is the work done on the object?

Accepted Answer

$$W = F d = 5 	imes 4 = 20\ \mathrm{J}$$

Question 9

A 100 W light bulb is left on for 2 hours. How much energy does it consume in joules?

Accepted Answer

$$E = P t = 100 	imes (2 	imes 3600) = 720,000\ \mathrm{J}$$

Question 10

A 0.5 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

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

Question 11

A block slides down a frictionless incline of height 3 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 3} = 7.67\ \mathrm{m/s}$$

Question 12

A 2 kg block is pushed by a constant force of 10 N across a rough surface for 5 m. The coefficient of kinetic friction is 0.2. What is the net work done on the block?

Accepted Answer

$$W_{net} = F d - \mu_k m g d = 10 	imes 5 - 0.2 	imes 2 	imes 9.8 	imes 5 = 50 - 19.6 = 30.4\ \mathrm{J}$$

Question 13

Which of the following best describes the normal force acting on a book resting on a horizontal table?

Accepted Answer

It is equal in magnitude and opposite in direction to the weight of the book.

Question 14

A 3 kg object moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of its acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{r} = \frac{16}{2} = 8\ \mathrm{m/s^2$}$$

Question 15

A spring with $$k = 100\ \mathrm{N/m} is $$compressed by 0.2 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = 0.5 	imes 100 	imes 0.04 = 2\ \mathrm{J}$$

Question 16

A 1 kg object is pulled up a 10 m ramp inclined at 30° to the horizontal at constant speed. If the coefficient of kinetic friction is 0.1, what is the total work done by the applied force?

Accepted Answer

$$W = m g h + \mu_k m g \cos	heta 	imes d = 1 	imes 9.8 	imes 5 + 0.1 	imes 1 	imes 9.8 	imes 0.866 	imes 10 = 49 + 8.5 = 57.5\ \mathrm{J}$$

Question 17

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

Accepted Answer

For every action, there is an equal and opposite reaction; the forces act on different objects.

Question 18

A 2 kg block is attached to a spring and oscillates on a frictionless surface. If the block is pulled 0.3 m from equilibrium and released, and the spring constant is $$k = 50\ \mathrm{N/m}$$, what is the maximum kinetic energy of the block?

Accepted Answer

$$K_{max} = \frac{1}{2} k x^2$ = 0.5 	imes 50 	imes 0.09 = 2.25\ \mathrm{J}$$

Question 19

A 10 kg box is pulled up a 5 m long ramp inclined at 37° to the horizontal with a constant velocity. If the coefficient of kinetic friction is 0.2, what is the magnitude of the friction force?

Accepted Answer

$$f_k = \mu_k m g \cos	heta = 0.2 	imes 10 	imes 9.8 	imes 0.7986 = 15.6\ \mathrm{N}$$

Exam #2 Study Guide: Newton's Laws, Forces, Work, Energy, and Conservation

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