Q: A $$1200\ \mathrm{kg}$$ car is pulling a $$500\ \mathrm{kg}$$ trailer along level ground. Friction of the road on the trailer is negligible. The car accelerates with an acceleration of $$1.3\ \mathrm{m/s^2$}. $$What is the force exerted by the car on the trailer?

$$F = m_{\text{trailer}} a = 500 \times 1.3 = 650\ \mathrm{N}$$

Q: In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. If a rider is towed at a constant speed by a rope that is at an angle of $$17^\circ$$ from horizontal, the tension in the rope is $$2100\ \mathrm{N}. $$The force of the sail on the rider is $$30^\circ$$ from horizontal. What is the weight of the rider?

$$W = T \sin 17^\circ + F_{\text{sail}} \sin 30^\circ = 545\ \mathrm{N}$$

Q: What minimum horizontal force must the monkey apply to start the box in motion? (Static friction coefficient $$\mu_s = 0.40)$$

$$F_{\text{min}} = \mu_s N = 0.40 \times 40.0 = 16.0\ \mathrm{N}$$

Q: After the box has started moving, what minimum horizontal force must the monkey apply to keep the box moving at constant velocity? (Kinetic friction coefficient $$\mu_k = 0.20)$$

$$F_{\text{min}} = \mu_k N = 0.20 \times 40.0 = 8.0\ \mathrm{N}$$

Q: If the monkey applies a horizontal force of $$18.0\ \mathrm{N}$$, what is the magnitude of the friction force once the box is moving?

$$f = \mu_k N = 0.20 \times 40.0 = 8.0\ \mathrm{N}$$

Q: A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it accelerates too strongly. The coefficients of kinetic and static friction between the box and the bed of the truck are $$0.335$$ and $$0.450$$, respectively. Starting from rest, what is the shortest time the truck could accelerate uniformly to $$37.0\ \mathrm{m/s}$$ ($$=82.8$$ mph) without causing the box to slide?

$$t = \dfrac{v}{\mu_s g} = \dfrac{37.0}{0.450 \times 9.8} = 8.4\ \mathrm{s}$$

Question 1

A large wrecking ball of mass $$m = 3840\ \mathrm{kg} is $$held in place by two light steel cables. If the cable $$T_B$$ makes an angle of $$40^\circ$$ with the vertical, what is the tension $$T_B in $$the cable?

Accepted Answer

$$T_B = \dfrac{mg}{\cos 40^\circ}$$

Question 2

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman catches it with his line and applies a horizontal force with magnitude of $$5.2\ \mathrm{N} to $$the box and produces an acceleration of magnitude $$2.90\ \mathrm{m/s^2$}$$, what is the mass of the box?

Accepted Answer

$$m = \dfrac{F}{a} = \dfrac{5.2}{2.90} = 1.8\ \mathrm{kg}$$

Question 3

A $$1200\ \mathrm{kg}$$ car is pulling a $$500\ \mathrm{kg}$$ trailer along level ground. Friction of the road on the trailer is negligible. The car accelerates with an acceleration of $$1.3\ \mathrm{m/s^2$}. $$What is the force exerted by the car on the trailer?

Accepted Answer

$$F = m_{	ext{trailer}} a = 500 	imes 1.3 = 650\ \mathrm{N}$$

Question 4

In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. If a rider is towed at a constant speed by a rope that is at an angle of $$17^\circ$$ from horizontal, the tension in the rope is $$2100\ \mathrm{N}. $$The force of the sail on the rider is $$30^\circ$$ from horizontal. What is the weight of the rider?

Accepted Answer

$$W = T \sin 17^\circ + F_{	ext{sail}} \sin 30^\circ = 545\ \mathrm{N}$$

Question 5

A box of bananas weighing $$40.0\ \mathrm{N}$$ rests on a horizontal surface. The coefficient of static friction between the box and the surface is $$0.40$$ and the coefficient of kinetic friction is $$0.20. If no $$horizontal force is applied to the box and the box is at rest, how large is the friction force exerted on the box?

Accepted Answer

$$f = 0\ \mathrm{N}$$

Question 6

A monkey applies a horizontal force of $$6.0\ \mathrm{N} to a $$box of bananas weighing $$40.0\ \mathrm{N}$$, which is initially at rest. What is the magnitude of the friction force?

Accepted Answer

$$f = 6.0\ \mathrm{N}$$

Question 7

What minimum horizontal force must the monkey apply to start the box in motion? (Static friction coefficient $$\mu_s = 0.40)$$

Accepted Answer

$$F_{	ext{min}} = \mu_s N = 0.40 	imes 40.0 = 16.0\ \mathrm{N}$$

Question 8

After the box has started moving, what minimum horizontal force must the monkey apply to keep the box moving at constant velocity? (Kinetic friction coefficient $$\mu_k = 0.20)$$

Accepted Answer

$$F_{	ext{min}} = \mu_k N = 0.20 	imes 40.0 = 8.0\ \mathrm{N}$$

Question 9

If the monkey applies a horizontal force of $$18.0\ \mathrm{N}$$, what is the magnitude of the friction force once the box is moving?

Accepted Answer

$$f = \mu_k N = 0.20 	imes 40.0 = 8.0\ \mathrm{N}$$

Question 10

If the monkey applies a horizontal force of $$18.0\ \mathrm{N}$$, what is the box's acceleration? (Box weight $$= 40.0\ \mathrm{N}$$, $$\mu_k = 0.20)$$

Accepted Answer

$$a = \dfrac{F - f_k}{m} = \dfrac{18.0 - 8.0}{40.0 / 9.8} = 2.5\ \mathrm{m/s^2$}$$

Question 11

A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it accelerates too strongly. The coefficients of kinetic and static friction between the box and the bed of the truck are $$0.335$$ and $$0.450$$, respectively. Starting from rest, what is the shortest time the truck could accelerate uniformly to $$37.0\ \mathrm{m/s}$$ ($$=82.8$$ mph) without causing the box to slide?

Accepted Answer

$$t = \dfrac{v}{\mu_s g} = \dfrac{37.0}{0.450 	imes 9.8} = 8.4\ \mathrm{s}$$

Question 12

A box of bananas weighing $$40.0\ \mathrm{N} is at $$rest on a horizontal surface. If a monkey applies a horizontal force of $$6.0\ \mathrm{N}$$, what is the acceleration of the box?

Accepted Answer

$$a = 0\ \mathrm{m/s^2$}$$

Question 13

A large wrecking ball is held in place by two cables. If the tension in the horizontal cable $$T_A is$$ $$3.1 	imes 10^3$\ \mathrm{N}$$, what is the horizontal component of the tension in the cable $$T_B$$ that makes an angle of $$40^\circ$$ with the vertical?

Accepted Answer

$$T_{B,x} = T_B \sin 40^\circ$$

Question 14

A fisherman pulls a box on a frictionless surface with a force of $$5.2\ \mathrm{N}$$, causing an acceleration of $$2.90\ \mathrm{m/s^2$}. If $$the fisherman doubles the force, what will be the new acceleration?

Accepted Answer

$$a = \dfrac{2 	imes 5.2}{1.8} = 5.8\ \mathrm{m/s^2$}$$

Question 15

A $$1200\ \mathrm{kg}$$ car pulls a $$500\ \mathrm{kg}$$ trailer. If the car and trailer accelerate at $$1.3\ \mathrm{m/s^2$}$$, what is the total force required to accelerate both?

Accepted Answer

$$F = (1200 + 500) 	imes 1.3 = 2210\ \mathrm{N}$$

Question 16

In parasailing, if the tension in the rope is $$2100\ \mathrm{N} at$$ $$17^\circ$$ above horizontal, and the force of the sail on the rider is $$545\ \mathrm{N} at$$ $$30^\circ$$ above horizontal, what is the vertical component of the total force supporting the rider?

Accepted Answer

$$F_{y} = 2100 \sin 17^\circ + 545 \sin 30^\circ$$

Forces and Motion: Study Notes and Problem Analysis

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