Q: A 1500 kg car is pulled by a tow truck with a tension of 2500 N, and a friction force of 200 N opposes the motion. What is the car’s speed after 5.0 seconds, starting from rest?

$$v = \frac{2500 - 200}{1500} \times 5 = 7.67\ \text{m/s}$$

Q: A construction worker with a weight of 850 N stands on a roof sloped at 30°. What is the magnitude of the normal force exerted by the roof?

$$F_n = 850 \times \cos(30^\circ) = 736.1\ \text{N}$$

Q: A 500 g model rocket is launched straight up. The rocket motor burns for 5.00 s with a steady thrust of 20.0 N. What is the maximum altitude reached by the rocket? (Neglect air resistance)

$$a = \frac{20.0 - 0.5 \times 9.8}{0.5} = 30.2\ \text{m/s}^2$$; $$h = \frac{1}{2} a t^2$ = 378\ \text{m}$$

Q: A car with a weight of 15,000 N is being towed up a 20° slope at constant velocity. Friction is negligible. The tow rope is rated at 6000 N maximum tension. Will it break?

No, because the tension required is $$T = 15,000 \times \sin(20^\circ) = 5130\ \text{N}$$, which is less than 6000 N.

Q: A loudspeaker weighing 10 kg is suspended 2 m below the ceiling by two 3-m-long cables that angle outward at equal angles. What is the tension in each cable?

$$T = \frac{mg}{2 \cos \theta}$$, where $$\theta = \cos$$^{-1}$$(2/3)$$; $$T \approx 61.3\ \text{N}$$

Q: A football coach sits on a sled while two players drag the sled across the field with ropes at a 20° angle between them. The frictional force is 2000 N. How hard must each player pull to move the sled at steady speed?

$$F = \frac{2000}{2 \cos(10^\circ)} = 1013\ \text{N}$$

Question 1

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

Accepted Answer

An object at rest will remain at rest, and an object in motion will continue moving in a straight line with constant velocity if the net force acting on it is zero.

Question 2

A 1500 kg car is pulled by a tow truck with a tension of 2500 N, and a friction force of 200 N opposes the motion. What is the car’s speed after 5.0 seconds, starting from rest?

Accepted Answer

$$v = \frac{2500 - 200}{1500} 	imes 5 = 7.67\ 	ext{m/s}$$

Question 3

Which of the following is NOT a contact force?

Accepted Answer

Gravity

Question 4

A construction worker with a weight of 850 N stands on a roof sloped at 30°. What is the magnitude of the normal force exerted by the roof?

Accepted Answer

$$F_n = 850 	imes \cos(30^\circ) = 736.1\ 	ext{N}$$

Question 5

Which statement about mass and weight is correct?

Accepted Answer

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

Question 6

A 500 g model rocket is launched straight up. The rocket motor burns for 5.00 s with a steady thrust of 20.0 N. What is the maximum altitude reached by the rocket? (Neglect air resistance)

Accepted Answer

$$a = \frac{20.0 - 0.5 	imes 9.8}{0.5} = 30.2\ 	ext{m/s}^2$$; $$h = \frac{1}{2} a t^2$ = 378\ 	ext{m}$$

Question 7

Which of the following best describes the net force acting on an object moving at constant velocity?

Accepted Answer

The net force is zero.

Question 8

A skier is being towed up a snow-covered hill by a rope. Which forces act on the skier?

Accepted Answer

Gravity, tension, normal force, friction

Question 9

A bungee jumper is nearing the bottom of her fall. Which forces are acting on her?

Accepted Answer

Gravity and spring force

Question 10

A car with a weight of 15,000 N is being towed up a 20° slope at constant velocity. Friction is negligible. The tow rope is rated at 6000 N maximum tension. Will it break?

Accepted Answer

No, because the tension required is $$T = 15,000 	imes \sin(20^\circ) = 5130\ 	ext{N}$$, which is less than 6000 N.

Question 11

Which of the following is a correct application of Newton’s Third Law?

Accepted Answer

When you push against a wall, the wall pushes back with an equal and opposite force.

Question 12

A loudspeaker weighing 10 kg is suspended 2 m below the ceiling by two 3-m-long cables that angle outward at equal angles. What is the tension in each cable?

Accepted Answer

$$T = \frac{mg}{2 \cos 	heta}$$, where $$	heta = \cos$$^{-1}$$(2/3)$$; $$T \approx 61.3\ 	ext{N}$$

Question 13

A football coach sits on a sled while two players drag the sled across the field with ropes at a 20° angle between them. The frictional force is 2000 N. How hard must each player pull to move the sled at steady speed?

Accepted Answer

$$F = \frac{2000}{2 \cos(10^\circ)} = 1013\ 	ext{N}$$

Question 14

Which force is responsible for the resistance experienced by a car moving through air?

Accepted Answer

Drag force

Question 15

A man has a mass of 69 kg. What is his weight on Mars, where $$g = 3.76\ 	ext{m/s}^2$$?

Accepted Answer

$$W = 69 	imes 3.76 = 259\ 	ext{N}$$

Question 16

Which of the following is the correct formula for Newton’s Second Law?

Accepted Answer

$$F = m 	imes a$$

Question 17

A 2.0 kg object is acted upon by forces such that the net force in the x-direction is 6 N and in the y-direction is 8 N. What are the x- and y-components of the object's acceleration?

Accepted Answer

$$a_x = 3\ 	ext{m/s}^2$$, $$a_y = 4\ 	ext{m/s}^2$$

Question 18

Which of the following is a correct statement about friction?

Accepted Answer

Static friction acts to prevent slipping.

Newton’s Laws and Forces: Calculus-Based Physics for Engineers

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