Q: 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?

$$x = \frac{v^2$}{2a} = \frac{(4.5)^2$}{2 \times 0.6} = 16.9\ \mathrm{m}$$

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?

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

Q: A 980 N object hangs from a rope and accelerates upward at $$5\ \mathrm{m/s^2$}. $$What is the tension in the rope?

$$T = mg + ma = 980 + 100 \times 5 = 1480\ \mathrm{N}$$

Q: A 0.046 kg golf ball is putted with a speed of 3.0 m/s. Friction exerts a force of 0.020 N. Using kinematics, what is the distance the ball travels before stopping?

$$x = \frac{v^2$}{2a} = \frac{(3.0)^2$}{2 \times 0.435} = 10.3\ \mathrm{m}$$

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

$$x = \frac{v^2$}{2a} = \frac{(4.5)^2$}{2 	imes 0.6} = 16.9\ \mathrm{m}$$

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

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

Question 5

A 100 kg crate is pulled by a rope at an angle of 20° above the horizontal. If the crate is moving at constant velocity and the friction force is 320 N, what is the tension in the rope?

Accepted Answer

$$T = \frac{f}{\cos 20^\circ} = \frac{320}{0.94} = 340\ \mathrm{N}$$

Question 6

A 980 N object hangs from a rope and accelerates upward at $$5\ \mathrm{m/s^2$}. $$What is the tension in the rope?

Accepted Answer

$$T = mg + ma = 980 + 100 	imes 5 = 1480\ \mathrm{N}$$

Question 7

Which of the following is NOT a correct step in solving a Newton’s Second Law problem?

Accepted Answer

Ignore friction forces if they are small.

Question 8

A ball is rolling to the right and slows down due to friction. In the free-body diagram, which direction does the acceleration vector point?

Accepted Answer

To the left, opposite to the velocity.

Question 9

If the net force on an object is zero, what can be said about its acceleration?

Accepted Answer

The acceleration is zero.

Question 10

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

Accepted Answer

$$x = \frac{v^2$}{2a} = \frac{(3.0)^2$}{2 	imes 0.435} = 10.3\ \mathrm{m}$$

Question 11

Which equation would you use to find the final position of an object given its initial velocity, acceleration, and time?

Accepted Answer

$$x_f = x_i + v_{x,i} t + \frac{1}{2} a_x t^2$

Question 12

A car accelerates from rest to 12 m/s in 10 s. What is its acceleration?

Accepted Answer

$$a = \frac{12}{10} = 1.2\ \mathrm{m/s^2$}$$

Question 13

In Newton’s Second Law, what does the term $$\sum F_x$$ represent?

Accepted Answer

The sum of all forces acting in the x-direction.

Question 14

A 1500 kg car is being towed and accelerates at $$1.2\ \mathrm{m/s^2$}. If $$the friction force is 320 N, what is the net force acting on the car?

Accepted Answer

$$F_{net} = m a = 1500 	imes 1.2 = 1800\ \mathrm{N}$$

Question 15

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

Accepted Answer

They show all the forces acting on an object.

Question 16

A block is pulled across a surface with a constant velocity. What can be said about the net force acting on the block?

Accepted Answer

The net force is zero.

Question 17

Which of the following is a real-world example of Newton’s Second Law?

Accepted Answer

A car accelerating when you press the gas pedal.

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

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