Q: A car of mass 1500 kg is being towed by a rope at a 20° angle above the horizontal. The car accelerates from rest to 12 m/s in 10 s, and a friction force of 320 N opposes its motion. What is the magnitude of the tension in the rope?

$$T = \frac{m a + f}{\cos 20^\circ} = \frac{1500 \times 1.2 + 320}{\cos 20^\circ} = 2300\ \mathrm{N}$$

Q: A 100 kg object hangs from a rope and accelerates upward at 5 m/s². What is the tension in the rope?

$$T = m(g + a) = 100 \times (9.8 + 5) = 1480\ \mathrm{N}$$

Question 1

A 0.046 kg golf ball is putted with an initial speed of 3.0 m/s. If friction exerts a force of 0.020 N opposite to the motion, what is the acceleration of the ball?

Accepted Answer

$$a = \frac{-0.020}{0.046} = -0.435\ \mathrm{m/s^2$}$$

Question 2

Which of the following correctly expresses Newton’s Second Law in component form?

Accepted Answer

$$\sum F_x = m a_x$$\ and\ $$\sum F_y = m a_y$$

Question 3

A 20 kg sled slides across frictionless ice at 4.5 m/s and then hits snow, which exerts a friction force of 12 N. How far does the sled travel in the snow before coming to rest?

Accepted Answer

Question 4

A car of mass 1500 kg is being towed by a rope at a 20° angle above the horizontal. The car accelerates from rest to 12 m/s in 10 s, and a friction force of 320 N opposes its motion. What is the magnitude of the tension in the rope?

Accepted Answer

$$T = \frac{m a + f}{\cos 20^\circ} = \frac{1500 	imes 1.2 + 320}{\cos 20^\circ} = 2300\ \mathrm{N}$$

Question 5

A 100 kg object hangs from a rope and accelerates upward at 5 m/s². What is the tension in the rope?

Accepted Answer

$$T = m(g + a) = 100 	imes (9.8 + 5) = 1480\ \mathrm{N}$$

Question 6

In the golf ball example, why is the acceleration in the y-direction zero?

Accepted Answer

Because the ball is rolling on a flat surface and there is no net force in the y-direction.

Question 7

Which step is NOT part of the recommended problem-solving approach for Newton’s Second Law problems?

Accepted Answer

Ignore the direction of acceleration when using kinematics.

Question 8

A 50 kg box is pulled across a horizontal floor with a force of 200 N at an angle of 30° above the horizontal. If the friction force is 80 N, what is the acceleration of the box?

Accepted Answer

$$a = \frac{200 \cos 30^\circ - 80}{50} = 2.1\ \mathrm{m/s^2$}$$

Question 9

Which of the following is a correct application of Newton’s Second Law to find the net force on an object?

Accepted Answer

$$F_{net} = m a$$

Question 10

A 10 kg object is acted upon by two forces: 30 N to the right and 10 N to the left. What is the acceleration of the object?

Accepted Answer

$$a = \frac{30 - 10}{10} = 2\ \mathrm{m/s^2$}$$

Question 11

A 5 kg object is dropped from rest and falls under gravity. What is its acceleration?

Accepted Answer

$$a = 9.8\ \mathrm{m/s^2$}$$

Question 12

A 980 N object is hanging by a rope at an angle of 20°. What is the tension in the rope?

Accepted Answer

$$T = \frac{980}{\cos 20^\circ} = 1042\ \mathrm{N}$$

Question 13

Which of the following statements about free-body diagrams is correct?

Accepted Answer

They show all the forces acting on an object and help determine the net force.

Question 14

A 0.046 kg golf ball is putted with a speed of 3.0 m/s. Friction exerts a force of 0.020 N. What is the distance the ball travels before stopping?

Accepted Answer

Question 15

Which of the following is a common mistake when applying Newton’s Second Law?

Accepted Answer

Forgetting to include all forces in the free-body diagram.

Question 16

A 2 kg object is pushed with a net force of 10 N. What is its acceleration?

Accepted Answer

$$a = \frac{10}{2} = 5\ \mathrm{m/s^2$}$$

Question 17

If the sum of the forces in the x-direction is zero, what can be said about the acceleration in the x-direction?

Accepted Answer

The acceleration in the x-direction is zero.

Question 18

A 10 kg object is at rest on a horizontal surface. What is the normal force acting on it?

Accepted Answer

$$N = m g = 10 	imes 9.8 = 98\ \mathrm{N}$$

Dynamics and Newton’s Second Law: Problem-Solving in College Physics

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