Q: A skier of mass 65 kg skis down a frictionless slope inclined at 32° to the horizontal. What is the component of the gravitational force acting parallel to the slope?

$$F_{\parallel} = mg \sin \theta = 65\ \mathrm{kg} \times 9.8\ \mathrm{m/s^2$} \times \sin 32^\circ \approx 336\ \mathrm{N}$$

Q: A crate of mass 6.00 kg is connected to a 4.00 kg crate by a rope. A horizontal force of 20 N is applied to the 6.00 kg crate. Ignoring friction, what is the acceleration of the system?

$$a = \frac{F}{m_{\text{total}}} = \frac{20\ \mathrm{N}}{6.00\ \mathrm{kg} + 4.00\ \mathrm{kg}} = 2.0\ \mathrm{m/s^2$}$$

Q: A person stands on a scale inside an elevator that is accelerating upward at $$0.90\ \mathrm{m/s^2$}. If $$the person's mass is 50 kg, what does the scale read?

$$n = m(a_y + g) = 50\ \mathrm{kg} \times (0.90 + 9.8)\ \mathrm{m/s^2$} = 535\ \mathrm{N}$$

Q: A ketchup bottle of mass 0.5 kg slides on a countertop and comes to rest after traveling 1.0 m. If its initial speed was 2.0 m/s, what is the magnitude of the friction force acting on the bottle?

$$f = m a_x = 0.5\ \mathrm{kg} \times 2.0\ \mathrm{m/s^2$} = 1.0\ \mathrm{N}$$

Question 1

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

Accepted Answer

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

Question 2

A 10-N force is applied at an angle of 30° above the horizontal. What are the horizontal ($$F_x) $$and vertical ($$F_y) $$components of the force?

Accepted Answer

$$F_x = 10 \cos 30^\circ = 8.66\ \mathrm{N}$$, $$F_y = 10 \sin 30^\circ = 5.0\ \mathrm{N}$$

Question 3

A block of mass 40 kg is pushed with a constant horizontal force of 20 N on a frictionless surface. What is the acceleration of the block?

Accepted Answer

$$a = \frac{F}{m} = \frac{20\ \mathrm{N}}{40\ \mathrm{kg}} = 0.5\ \mathrm{m/s^2$}$$

Question 4

Which of the following is NOT a contact force?

Accepted Answer

Weight (gravitational force)

Question 5

A skier of mass 65 kg skis down a frictionless slope inclined at 32° to the horizontal. What is the component of the gravitational force acting parallel to the slope?

Accepted Answer

$$F_{\parallel} = mg \sin 	heta = 65\ \mathrm{kg} 	imes 9.8\ \mathrm{m/s^2$} 	imes \sin 32^\circ \approx 336\ \mathrm{N}$$

Question 6

A crate of mass 6.00 kg is connected to a 4.00 kg crate by a rope. A horizontal force of 20 N is applied to the 6.00 kg crate. Ignoring friction, what is the acceleration of the system?

Accepted Answer

$$a = \frac{F}{m_{	ext{total}}} = \frac{20\ \mathrm{N}}{6.00\ \mathrm{kg} + 4.00\ \mathrm{kg}} = 2.0\ \mathrm{m/s^2$}$$

Question 7

A person stands on a scale inside an elevator that is accelerating upward at $$0.90\ \mathrm{m/s^2$}. If $$the person's mass is 50 kg, what does the scale read?

Accepted Answer

$$n = m(a_y + g) = 50\ \mathrm{kg} 	imes (0.90 + 9.8)\ \mathrm{m/s^2$} = 535\ \mathrm{N}$$

Question 8

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

Accepted Answer

If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

Question 9

A block is being lifted at a constant speed by a cable. Which statement is true about the forces acting on the block?

Accepted Answer

The upward tension force equals the downward gravitational force.

Question 10

A ketchup bottle of mass 0.5 kg slides on a countertop and comes to rest after traveling 1.0 m. If its initial speed was 2.0 m/s, what is the magnitude of the friction force acting on the bottle?

Accepted Answer

$$f = m a_x = 0.5\ \mathrm{kg} 	imes 2.0\ \mathrm{m/s^2$} = 1.0\ \mathrm{N}$$

Question 11

Two horizontal forces act on a 4 kg block on a frictionless surface: $$\vec{F}_1 = -4\hat{j}\ \mathrm{N}$$ and $$\vec{F}_2 = -5\hat{i} + \hat{j}\ \mathrm{N}. $$What is the magnitude of the block's acceleration?

Accepted Answer

$$a = \sqrt{(-1.25)^2$ + (0.25)^2$} = 1.27\ \mathrm{m/s^2$}$$

Question 12

A block of mass $$m$$ hangs from two cables, each making a 45° angle with the ceiling. What is the tension in each cable?

Accepted Answer

$$T = \frac{mg}{2 \sin 45^\circ} = \frac{mg}{\sqrt{2}}$$

Question 13

A person stands on a scale in an elevator that is in free fall. What does the scale read?

Accepted Answer

Zero; the person feels weightless because the normal force is zero.

Question 14

Which of the following is true about action-reaction pairs according to Newton's Third Law?

Accepted Answer

They act on two different objects and are equal in magnitude and opposite in direction.

Question 15

A box is pushed with a constant force on a rough surface and moves at constant velocity. What can be said about the net force acting on the box?

Accepted Answer

The net force is zero; the applied force is balanced by friction.

Question 16

A block of mass 2.00 kg is accelerated upward at $$3.00\ \mathrm{m/s^2$} by an $$upward force. What is the magnitude of the upward force?

Accepted Answer

$$F = m(a + g) = 2.00\ \mathrm{kg} 	imes (3.00 + 9.8)\ \mathrm{m/s^2$} = 25.6\ \mathrm{N}$$

Question 17

A horse pulls a wagon. According to Newton's Third Law, which statement is correct?

Accepted Answer

The force the horse exerts on the wagon is equal in magnitude and opposite in direction to the force the wagon exerts on the horse.

Question 18

A block is acted upon by three forces: $$F_1 = 50$$\ \mathrm{N}$$ to the right, F_2$ = 120\ \mathrm{N}$$ downward, and $$F_3 = 250$$\ \mathrm{N}$$ at 53° above the negative x-axis. What is the magnitude of the net force?

Accepted Answer

$$F_{	ext{net}} = \sqrt{(-100)^2$ + (80)^2$} = 128\ \mathrm{N}$$

CH4-Newton's Laws of Motion and Forces: EXAM 2

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