Q: A traffic light of mass $$m$$ hangs from three cables as shown in the diagram, with $$T_1 at$$ $$37^ ext{o} to $$the horizontal, $$T_2 at$$ $$53^ ext{o} to $$the horizontal, and $$T_3$$ vertically upward. If the system is in equilibrium, which equation correctly represents the sum of the forces in the vertical ($$y) $$direction?

$$T_1$$ \sin 37^\text{o} + $$T_2$$ \sin 53^\text{o} - mg = 0$$

Q: A block of mass $$m$$ slides down a rough inclined plane of angle $$\theta$$ with a coefficient of kinetic friction $$\mu_k. $$What is the acceleration $$a of $$the block?

$$a = g(\sin \theta - \mu_k \cos \theta)$$

Q: A 10 kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is $$\mu_s = 0.5. $$What is the minimum horizontal force required to start moving the box?

$$F = 10 \times 9.8 \times 0.5 = 49\ \text{N}$$

Q: A 5 kg block is connected by a light string over a frictionless pulley to a 3 kg block. What is the tension $$T in $$the string?

$$T = \dfrac{2}{8} \times 9.8 + 3 \times 9.8 = 7.35\ \text{N} + 29.4\ \text{N} = 36.75\ \text{N}$$

Q: A block is sliding down a plane inclined at $$30^\text{o} to $$the horizontal. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the net force acting on a 2 kg block?

$$F = 2 \times 9.8 \times (\sin 30^\text{o} - 0.2 \cos 30^\text{o})$$

Question 1

A traffic light of mass $$m$$ hangs from three cables as shown in the diagram, with $$T_1 at$$ $$37^	ext{o} to $$the horizontal, $$T_2 at$$ $$53^	ext{o} to $$the horizontal, and $$T_3$$ vertically upward. If the system is in equilibrium, which equation correctly represents the sum of the forces in the vertical ($$y) $$direction?

Accepted Answer

$$T_1$$ \sin 37^	ext{o} + $$T_2$$ \sin 53^	ext{o} - mg = 0$$

Question 2

A car of mass $$m is $$parked on a frictionless incline at angle $$	heta. $$What is the magnitude of the normal force $$n$$ exerted by the plane on the car?

Accepted Answer

$$n = mg \cos 	heta$$

Question 3

In an Atwood's machine, two masses $$m_1$$ and $$m_2$$ are connected by a light, inextensible string over a frictionless, massless pulley. If $$m_1$$ \u003e $$m_2$$, what is the acceleration $$a of $$the system?

Accepted Answer

$$a = \dfrac{(m_1$ - m_2$)g}{m_1$ + m_2$}$$

Question 4

A block of mass $$m$$ slides down a rough inclined plane of angle $$	heta$$ with a coefficient of kinetic friction $$\mu_k. $$What is the acceleration $$a of $$the block?

Accepted Answer

$$a = g(\sin 	heta - \mu_k \cos 	heta)$$

Question 5

Which of the following statements about friction is correct?

Accepted Answer

The coefficient of friction is nearly independent of the area of contact between surfaces.

Question 6

A 10 kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is $$\mu_s = 0.5. $$What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$F = 10 	imes 9.8 	imes 0.5 = 49\ 	ext{N}$$

Question 7

A block is at rest on a horizontal surface. As you gradually increase the applied horizontal force, the frictional force:

Accepted Answer

Increases up to a maximum value, then drops when the block starts moving.

Question 8

A sled of mass $$m is $$pulled at constant speed across a horizontal surface with coefficient of kinetic friction $$\mu_k. $$What is the magnitude of the pulling force $$F$$ required?

Accepted Answer

$$F = \mu_k m g$$

Question 9

Which of the following best describes the condition for equilibrium of a particle?

Accepted Answer

The sum of all forces acting on the particle is zero.

Question 10

A 5 kg block is connected by a light string over a frictionless pulley to a 3 kg block. What is the tension $$T in $$the string?

Accepted Answer

$$T = \dfrac{2}{8} 	imes 9.8 + 3 	imes 9.8 = 7.35\ 	ext{N} + 29.4\ 	ext{N} = 36.75\ 	ext{N}$$

Question 11

A block is sliding down a plane inclined at $$30^	ext{o} to $$the horizontal. If the coefficient of kinetic friction is $$\mu_k = 0.2$$, what is the net force acting on a 2 kg block?

Accepted Answer

$$F = 2 	imes 9.8 	imes (\sin 30^	ext{o} - 0.2 \cos 30^	ext{o})$$

Question 12

Which of the following is true about the tension in the string of an ideal Atwood's machine (massless, frictionless pulley)?

Accepted Answer

The tension is the same on both sides of the pulley.

Question 13

A block is on the verge of sliding down a rough incline. The angle of the incline is $$	heta. $$What is the coefficient of static friction $$\mu_s$$?

Accepted Answer

$$\mu_s = 	an 	heta$$

Question 14

A 2 kg block is pushed up a $$20^	ext{o}$$ incline with a force parallel to the incline. The coefficient of kinetic friction is $$0.3. $$What is the minimum force required to move the block up at constant speed?

Accepted Answer

$$F = 2 	imes 9.8 	imes (\sin 20^	ext{o} + 0.3 \cos 20^	ext{o})$$

Question 15

Which of the following is NOT a correct statement about friction?

Accepted Answer

The force of friction is always independent of the normal force.

Question 16

A 50 kg crate is being pulled across a warehouse floor with a coefficient of kinetic friction $$\mu_k = 0.25. $$What is the frictional force acting on the crate?

Accepted Answer

$$f_k = 50 	imes 9.8 	imes 0.25 = 122.5\ 	ext{N}$$

Question 17

If a block is sliding at constant speed down an incline, what can you conclude about the net force acting on it?

Accepted Answer

The net force is zero.

Question 18

A 3 kg block is connected to a 2 kg block by a light string over a frictionless pulley. If the system is released from rest, what is the acceleration of the blocks?

Accepted Answer

$$a = \dfrac{(3 - 2) 	imes 9.8}{3 + 2} = 1.96\ 	ext{m/s}^2$$

(CH5) Applying Newton's Laws: Equilibrium, Multiple Objects, and Friction

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