Q: A 10 kg object is suspended from a spring. The spring stretches by 0.25 m. If the spring constant is $$k = 400\ \mathrm{N/m}$$, what is the magnitude of the spring force?

$$F = kx = 400 \times 0.25 = 100\ \mathrm{N}$$

Q: A 65-kg woman stands on a scale in an elevator accelerating downward at $$0.20g. $$What does the scale read?

$$F_N = m(g - 0.20g) = 65 \times 0.8 \times 9.8 = 509.6\ \mathrm{N}$$

Q: A car of mass 1500 kg is brought to rest from 100 km/h in 55 m. What is the average net force required? (Assume $$v_0 = 100$$\ \mathrm{km/h} = 27.78\ \mathrm{m/s}$$, v = 0$)

$$F = m a = m \frac{v^2$ - v_0$^2}{2x} = 1500 \times \frac{0^2$ - 27.78^2$}{2 \times 55} = -10500\ \mathrm{N}$$

Q: A 10 kg box is resting on a table. If a person pushes down on the box with a force of 40 N, what is the normal force exerted by the table?

$$F_N = mg + 40 = 10 \times 9.8 + 40 = 138\ \mathrm{N}$$

Question 1

A 5.0 kg box is at rest on a frictionless horizontal table. A horizontal force of 20 N is applied to the box. What is the acceleration of the box?

Accepted Answer

$$a = \frac{20}{5.0} = 4.0\ \mathrm{m/s^2$}$$

Question 2

A 10 kg object is suspended from a spring. The spring stretches by 0.25 m. If the spring constant is $$k = 400\ \mathrm{N/m}$$, what is the magnitude of the spring force?

Accepted Answer

$$F = kx = 400 	imes 0.25 = 100\ \mathrm{N}$$

Question 3

A hockey puck slides at constant velocity across a frictionless ice surface. Which statement is true about the net force acting on the puck?

Accepted Answer

The net force is zero because there is no change in velocity.

Question 4

A 65-kg woman stands on a scale in an elevator accelerating downward at $$0.20g. $$What does the scale read?

Accepted Answer

$$F_N = m(g - 0.20g) = 65 	imes 0.8 	imes 9.8 = 509.6\ \mathrm{N}$$

Question 5

Which of the following is NOT a contact force?

Accepted Answer

Gravitational force (weight)

Question 6

A box of mass $$m is $$resting on a table. If the box is at rest, what is the relationship between the normal force $$F_N$$ and the weight $$w$$?

Accepted Answer

$$F_N = w = mg$$

Question 7

A car of mass 1500 kg is brought to rest from 100 km/h in 55 m. What is the average net force required? (Assume $$v_0 = 100$$\ \mathrm{km/h} = 27.78\ \mathrm{m/s}$$, v = 0$)

Accepted Answer

$$F = m a = m \frac{v^2$ - v_0$^2}{2x} = 1500 	imes \frac{0^2$ - 27.78^2$}{2 	imes 55} = -10500\ \mathrm{N}$$

Question 8

Which of the following best describes Newton's First Law?

Accepted Answer

An object will remain at rest or move at constant velocity unless acted upon by a net force.

Question 9

A 12.0 kg box and a 10.0 kg box are connected by a cord and pulled by a 40.0 N force on the 10.0 kg box. What is the acceleration of the system?

Accepted Answer

$$a = \frac{F}{m_{total}} = \frac{40.0}{12.0 + 10.0} = 1.82\ \mathrm{m/s^2$}$$

Question 10

A person pushes a box on ice. The box accelerates. Which force diagram best represents the forces acting on the box?

Accepted Answer

A horizontal push force, a vertical normal force, and a vertical weight force.

Question 11

A spring is compressed by 0.10 m and exerts a force of 30 N. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{F}{x} = \frac{30}{0.10} = 300\ \mathrm{N/m}$$

Question 12

A 10 kg box is resting on a table. If a person pushes down on the box with a force of 40 N, what is the normal force exerted by the table?

Accepted Answer

$$F_N = mg + 40 = 10 	imes 9.8 + 40 = 138\ \mathrm{N}$$

Question 13

Which of the following is a correct statement of Newton's Third Law?

Accepted Answer

Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first.

Question 14

A rocket is propelled upward by expelling hot gases downward. According to Newton's Third Law, what is the reaction force?

Accepted Answer

The upward force on the rocket by the expelled gases.

Question 15

A small mass $$m$$ hangs from a string in a car. When the car accelerates at $$a$$, the string makes an angle $$	heta$$ with the vertical. Which equation relates $$	heta to$$ $$a$$ and $$g$$?

Accepted Answer

$$	an 	heta = \frac{a}{g}$$

Question 16

Which of the following is true about mass and weight?

Accepted Answer

Mass is constant regardless of location, but weight depends on the gravitational field.

Question 17

A box is pulled by two ropes at angles of $$30^\circ$$ and $$60^\circ to $$the horizontal, each with a force of 50 N. What is the net force in the horizontal direction?

Accepted Answer

$$F_{net,x} = 50 \cos 30^\circ + 50 \cos 60^\circ = 43.3 + 25 = 68.3\ \mathrm{N}$$

Question 18

A mover uses a rope looped over two pulleys to slowly lift a piano of weight 2000 N. What force must he exert on the rope (neglecting friction)?

Accepted Answer

$$F = \frac{W}{2} = \frac{2000}{2} = 1000\ \mathrm{N}$$

Dynamics: Newton’s Laws of Motion – Study Notes

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