Q: A 10 kg traffic light is suspended by two cables, one making a 20° angle and the other a 40° angle with the horizontal. What is the tension in the cable at 40°?

$$T_2$$ = \frac{10 \times 9.81}{\cos 40^\circ (\tan 20^\circ + \tan 40^\circ)} = 106.4\ \mathrm{N}$$

Q: If a cart weighing 70 kg is acted upon by two forces, $$F_1 = 100$$\ \mathrm{N}$$ at 60° and F_2$ = 140\ \mathrm{N} at 30$$°, what is the magnitude of its acceleration?

$$|\vec{a}| = \frac{1}{70} \times 171 = 2.44\ \mathrm{m/s^2$}$$

Q: A 5.0 kg box is in contact with a 20.0 kg box on a frictionless surface. A horizontal force of 250 N is applied to the 20.0 kg box. What is the force that the 20.0 kg box exerts on the 5.0 kg box?

$$F = (5.0\ \mathrm{kg}) \times (10\ \mathrm{m/s^2$}) = 50\ \mathrm{N}$$

Q: A 10 kg traffic light is suspended by two cables at angles 20° and 40° with the horizontal. What is the sum of the vertical components of the tensions?

$$T_1$$ \sin 20^\circ + $$T_2$$ \sin 40^\circ = 10 \times 9.81$$

Question 1

A 12.0 kg sled is pulled with a force of 45.0 N at an angle of 30° above the horizontal. What is the horizontal component of the pulling force?

Accepted Answer

$$F_x = 45.0 \cos 30^\circ = 38.97\ \mathrm{N}$$

Question 2

A 10 kg traffic light is suspended by two cables, one making a 20° angle and the other a 40° angle with the horizontal. What is the tension in the cable at 40°?

Accepted Answer

$$T_2$$ = \frac{10 	imes 9.81}{\cos 40^\circ (	an 20^\circ + 	an 40^\circ)} = 106.4\ \mathrm{N}$$

Question 3

If a cart weighing 70 kg is acted upon by two forces, $$F_1 = 100$$\ \mathrm{N}$$ at 60° and F_2$ = 140\ \mathrm{N} at 30$$°, what is the magnitude of its acceleration?

Accepted Answer

$$|\vec{a}| = \frac{1}{70} 	imes 171 = 2.44\ \mathrm{m/s^2$}$$

Question 4

Which of the following best describes Newton’s Third Law in the context of the action-reaction diagram shown?

Accepted Answer

For every force exerted by one object on another, there is an equal and opposite force exerted back by the second object.

Question 5

A block is pulled along a rough surface with a force at an angle of 42° above the horizontal. If the coefficients of friction are $$\mu_s = 0.9$$ and $$\mu_k = 0.7$$, which equation gives the minimum force required to start moving the block?

Accepted Answer

$$F = \frac{\mu_s mg}{\cos 42^\circ + \mu_s \sin 42^\circ}$$

Question 6

A 30 kg sled is pulled horizontally on frictionless ice with a force of 180 N. What is its acceleration?

Accepted Answer

$$a = \frac{180}{30} = 6.0\ \mathrm{m/s^2$}$$

Question 7

In a free body diagram of a book resting on a table, which forces are present?

Accepted Answer

Weight (downward), normal force (upward), and any applied force.

Question 8

A 5.0 kg box is in contact with a 20.0 kg box on a frictionless surface. A horizontal force of 250 N is applied to the 20.0 kg box. What is the force that the 20.0 kg box exerts on the 5.0 kg box?

Accepted Answer

$$F = (5.0\ \mathrm{kg}) 	imes (10\ \mathrm{m/s^2$}) = 50\ \mathrm{N}$$

Question 9

Which statement about friction is correct?

Accepted Answer

Static friction must be overcome before an object starts to move.

Question 10

A traffic light of weight $$w$$ hangs from two cables, each making a 45° angle with the vertical. What is the tension in each cable?

Accepted Answer

$$T = \frac{w}{\sqrt{2}}$$

Question 11

A person pushes down on a book with a force $$F$$ while the book rests on a table. What is the normal force $$n$$ exerted by the table on the book?

Accepted Answer

$$n = w + F$$

Question 12

If a block is sliding on a surface with kinetic friction coefficient $$\mu_k$$, what is the frictional force acting on it?

Accepted Answer

$$f_k = \mu_k N$$

Question 13

A 10 kg traffic light is suspended by two cables at angles 20° and 40° with the horizontal. What is the sum of the vertical components of the tensions?

Accepted Answer

$$T_1$$ \sin 20^\circ + $$T_2$$ \sin 40^\circ = 10 	imes 9.81$$

Question 14

Which of the following is a correct application of the superposition principle in mechanics?

Accepted Answer

The net force on an object is the vector sum of all individual forces acting on it.

Question 15

A block is pulled along a rough surface. If the applied force is less than the maximum static friction, what happens?

Accepted Answer

The block does not move.

Question 16

In the context of free body diagrams, what does the length of an arrow represent?

Accepted Answer

The magnitude of the force.

Question 17

A person pulls a sled of mass $$m$$ with a force $$F at an $$angle $$	heta$$ above the horizontal. What is the vertical component of the pulling force?

Accepted Answer

$$F_y = F \sin 	heta$$

Question 18

Which of the following is NOT a correct statement about action-reaction pairs?

Accepted Answer

Action and reaction forces act on the same object.

Physics I: Mechanics – Action-Reaction Pairs and Friction

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