Q: A box of mass $$m$$ rests on a horizontal surface. You apply a force $$T at an $$angle $$\theta$$ above the horizontal. If the coefficients of static and kinetic friction are $$\mu_s$$ and $$\mu_k$$ respectively, what is the minimum force $$T$$ required to just start moving the box?

$$T = \frac{\mu_s m g}{\cos \theta + \mu_s \sin \theta}$$

Q: In an Atwood’s machine, a 28.0 kg counterweight and a load of bricks are suspended over a frictionless pulley. If the mass of the bricks is 31.0 kg, what is the acceleration of the system? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

$$a = \frac{g(m_2$ - m_1$)}{m_1$ + m_2$} = \frac{9.8 \times (31.0 - 28.0)}{31.0 + 28.0}$$

Q: A 5,000 kg pallet is pulled up a ramp at $$60^\circ$$ above the horizontal. The coefficient of friction is $$\mu = 0.95$$ and the cable’s breaking tension is 70,000 N. What is the maximum acceleration you can give the pallet without breaking the cable? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

$$a = \frac{T - m g \sin \theta - \mu m g \cos \theta}{m}$$

Q: A block of mass $$m is $$pulled up a ramp at angle $$\theta$$ with a force $$T. $$The coefficient of kinetic friction is $$\mu_k. $$What is the equation for the net force parallel to the ramp?

$$F_{\text{net}} = T - m g \sin \theta - \mu_k m g \cos \theta$$

Question 1

A box of mass $$m$$ rests on a horizontal surface. You apply a force $$T at an $$angle $$	heta$$ above the horizontal. If the coefficients of static and kinetic friction are $$\mu_s$$ and $$\mu_k$$ respectively, what is the minimum force $$T$$ required to just start moving the box?

Accepted Answer

$$T = \frac{\mu_s m g}{\cos 	heta + \mu_s \sin 	heta}$$

Question 2

In an Atwood’s machine, a 28.0 kg counterweight and a load of bricks are suspended over a frictionless pulley. If the mass of the bricks is 31.0 kg, what is the acceleration of the system? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{g(m_2$ - m_1$)}{m_1$ + m_2$} = \frac{9.8 	imes (31.0 - 28.0)}{31.0 + 28.0}$$

Question 3

A 5,000 kg pallet is pulled up a ramp at $$60^\circ$$ above the horizontal. The coefficient of friction is $$\mu = 0.95$$ and the cable’s breaking tension is 70,000 N. What is the maximum acceleration you can give the pallet without breaking the cable? (Use $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{T - m g \sin 	heta - \mu m g \cos 	heta}{m}$$

Question 4

Which statement best describes the difference between static and kinetic friction?

Accepted Answer

Static friction increases with applied force up to a maximum, while kinetic friction is nearly constant once motion starts.

Question 5

A sled of mass $$m$$ slides down a frictionless inclined plane at angle $$\alpha. $$What is the acceleration of the sled?

Accepted Answer

$$a = g \sin \alpha$$

Question 6

On an inclined plane with friction, the normal force $$n$$ acting on a box of mass $$m is $$given by:

Accepted Answer

$$n = m g \cos \alpha$$

Question 7

A box is at rest on a horizontal surface. You gradually increase the applied force $$T$$ until the box just begins to move. Which equation correctly relates the maximum static friction force $$f_{s,	ext{max}} to $$the normal force $$n$$?

Accepted Answer

$$f_{s,	ext{max}} = \mu_s n$$

Question 8

In uniform circular motion, the direction of the acceleration vector is:

Accepted Answer

Perpendicular to the velocity vector and points toward the center of the circle

Question 9

The magnitude of the centripetal acceleration for an object moving at speed $$v in a $$circle of radius $$R is$$:

Accepted Answer

$$a_c = \frac{v^2$}{R}$$

Question 10

A block of mass $$m$$ slides down an inclined plane of angle $$\alpha$$ with coefficient of kinetic friction $$\mu_k. $$What is the net acceleration of the block?

Accepted Answer

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

Question 11

In an Atwood’s machine, if both masses are equal, what is the acceleration of the system?

Accepted Answer

$$a = 0$$

Question 12

A block is moving at constant velocity on a rough surface. Which statement is true about the forces acting on it?

Accepted Answer

The applied force equals the kinetic friction force.

Question 13

A block of mass $$m is $$pulled up a ramp at angle $$	heta$$ with a force $$T. $$The coefficient of kinetic friction is $$\mu_k. $$What is the equation for the net force parallel to the ramp?

Accepted Answer

$$F_{	ext{net}} = T - m g \sin 	heta - \mu_k m g \cos 	heta$$

Question 14

Which of the following best describes the role of the normal force on an inclined plane?

Accepted Answer

It acts perpendicular to the surface and determines the maximum possible friction force.

Question 15

A block is at rest on a ramp. The angle of the ramp is gradually increased. At what angle $$	heta$$ will the block just begin to slide if the coefficient of static friction is $$\mu_s$$?

Accepted Answer

$$	heta = \arctan(\mu_s)$$

Question 16

In an Atwood’s machine, the tension in the rope while the load is moving is given by:

Accepted Answer

$$T = m_1$ a + m_1$ g$$

Question 17

A block of mass $$m is $$pulled along a rough surface with a force $$T at an $$angle $$	heta$$ above the horizontal. Which component of $$T$$ affects the normal force?

Accepted Answer

$$T \sin 	heta$$

Question 18

Which of the following is true about the kinetic friction force as shown in the friction graph?

Accepted Answer

It is essentially constant once the object is moving.

Question 19

A block slides down an inclined plane with friction. If the block moves at constant velocity, what is the relationship between the friction force $$f_k$$ and the component of gravity parallel to the plane?

Accepted Answer

$$f_k = m g \sin \alpha$$

Physics I: Mechanics – Friction, Ramps, Pulleys, and Circular Motion

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