Q: A 1500 kg car is being towed at a constant speed by a rope at a $$20^\circ$$ angle to the horizontal. The friction force opposing the motion is 320 N. What is the tension in the rope?

$$T = \frac{320}{\cos 20^\circ} = 340 \text{ N}$$

Q: A 70 kg person stands on a scale in an elevator accelerating upward. The scale reads 750 N. What is the elevator's acceleration?

$$a = \frac{750 - 686}{70} = 0.91 \text{ m/s}^2$$

Q: A 32 kg sofa is pushed at a steady speed across the floor using 'sofa sliders' with a coefficient of kinetic friction $$\mu_k = 0.080. $$What force does Carol apply to the sofa?

$$F = \mu_k m g = (0.080)(32)(9.8) = 25 \text{ N}$$

Q: A box with a weight of 100 N is at rest. It is then pulled by a horizontal force of 30 N. The coefficient of static friction is $$\mu_s = 0.40. $$Will the box move?

No, because $$30 \text{ N} \u003c \mu_s \times 100 \text{ N} = 40 \text{ N}$$

Q: A 0.046 kg golf ball is putted at 3.0 m/s and slowed by a friction force of 0.020 N. How far will it roll before stopping?

$$x = \frac{v^2$}{2a} = \frac{(3.0)^2$}{2 \times 0.435} = 10 \text{ m}$$

Q: A 1.2 kg book lies on a table. A hand presses down on the book with a force of 15 N. What is the normal force exerted by the table?

$$n = mg + F = 12 + 15 = 27 \text{ N}$$

Q: Two blocks, A (5 kg) and B (10 kg), are pushed together on a frictionless surface with a force of 30 N. What force does block A exert on block B?

$$F_{A \rightarrow B} = \frac{m_B}{m_A + m_B} F = \frac{10}{15} \times 30 = 20 \text{ N}$$

Question 1

A 500 N orangutan hangs motionless from a vertical rope. What is the tension in the rope?

Accepted Answer

$$T = 500 	ext{ N}$$

Question 2

A 1500 kg car is being towed at a constant speed by a rope at a $$20^\circ$$ angle to the horizontal. The friction force opposing the motion is 320 N. What is the tension in the rope?

Accepted Answer

$$T = \frac{320}{\cos 20^\circ} = 340 	ext{ N}$$

Question 3

A skier slides down a frictionless $$27^\circ$$ slope. What is the skier's acceleration?

Accepted Answer

$$a = g \sin 27^\circ$$

Question 4

A 70 kg person stands on a scale in an elevator accelerating upward. The scale reads 750 N. What is the elevator's acceleration?

Accepted Answer

$$a = \frac{750 - 686}{70} = 0.91 	ext{ m/s}^2$$

Question 5

A 32 kg sofa is pushed at a steady speed across the floor using 'sofa sliders' with a coefficient of kinetic friction $$\mu_k = 0.080. $$What force does Carol apply to the sofa?

Accepted Answer

$$F = \mu_k m g = (0.080)(32)(9.8) = 25 	ext{ N}$$

Question 6

A box with a weight of 100 N is at rest. It is then pulled by a horizontal force of 30 N. The coefficient of static friction is $$\mu_s = 0.40. $$Will the box move?

Accepted Answer

No, because $$30 	ext{ N} \u003c \mu_s 	imes 100 	ext{ N} = 40 	ext{ N}$$

Question 7

A 0.046 kg golf ball is putted at 3.0 m/s and slowed by a friction force of 0.020 N. How far will it roll before stopping?

Accepted Answer

$$x = \frac{v^2$}{2a} = \frac{(3.0)^2$}{2 	imes 0.435} = 10 	ext{ m}$$

Question 8

A 20 kg block slides along frictionless ice and then crosses a rough patch with a friction force of 12 N. How far does it travel before coming to rest if its initial speed is 5 m/s?

Accepted Answer

$$x = \frac{v^2$}{2a}$$, where $$a = \frac{f}{m} = \frac{12}{20} = 0.6 	ext{ m/s}^2$$, so $$x = \frac{25}{2 	imes 0.6} = 20.8 	ext{ m}$$

Question 9

A 1.2 kg book lies on a table. A hand presses down on the book with a force of 15 N. What is the normal force exerted by the table?

Accepted Answer

$$n = mg + F = 12 + 15 = 27 	ext{ N}$$

Question 10

A box is sitting on the floor of an elevator that is accelerating upward. The magnitude of the normal force on the box is:

Accepted Answer

$$n \u003e mg$$

Question 11

A block is being pulled to the right at steady speed by a rope that angles upward. In this situation, the normal force on the block is:

Accepted Answer

$$n \u003c mg$$

Question 12

A 100 kg stage set is lowered by a 100 kg stagehand who is hoisted upward when the rope is untied. What is the acceleration of the stagehand?

Accepted Answer

Question 13

A 0.020 kg mouse falls from a plane. If the drag force is $$D = C ho A v^2$ / 2$$ and at terminal speed $$D = mg$$, what is the mouse's terminal speed if $$C = 1.1$$, $$A = 2.1 	imes 10$$^{-3}$$ 	ext{ m}^2$$, $$ho = 1.2 	ext{ kg/m}^3$$?

Accepted Answer

$$v_t = \sqrt{\frac{2mg}{C \rho A}}$$

Question 14

Two blocks, A (5 kg) and B (10 kg), are pushed together on a frictionless surface with a force of 30 N. What force does block A exert on block B?

Accepted Answer

$$F_{A ightarrow B} = \frac{m_B}{m_A + m_B} F = \frac{10}{15} 	imes 30 = 20 	ext{ N}$$

Question 15

A box is being pulled to the right over a rough surface and is speeding up. Suddenly the rope breaks. What happens?

Accepted Answer

The box continues with the speed it had when the rope broke, then slows steadily until it stops.

Question 16

A 70 kg student stands on a scale in an elevator. The elevator cable breaks and the student falls. What does the scale read during the fall?

Accepted Answer

0 N

Question 17

A block is accelerated across a frictionless table by a falling mass $$m. $$The string is massless and the pulley is frictionless. The tension in the string is:

Accepted Answer

$$T \u003c mg$$

Question 18

Which of the following is always true for an action/reaction pair according to Newton's third law?

Accepted Answer

They are equal in magnitude and opposite in direction.

Chapter 5: Applying Newton's Laws – Equilibrium and Force Analysis

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