Q: A block of mass $$m$$ rests on an inclined plane with angle $$\theta. $$The coefficient of static friction between the block and the plane is $$\mu_s. $$What is the maximum angle $$\theta_{max}$$ before the block starts to slide?

$$\theta_{max} = \arctan(\mu_s)$$

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

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

Q: A 5 kg block is pulled across a horizontal surface with a constant velocity. The coefficient of kinetic friction is $$\mu_k = 0.2. $$What is the magnitude of the pulling force?

$$F = 0.2 \times 5 \times 9.8 = 9.8\ \mathrm{N}$$

Q: A block of mass $$m is $$pulled up a rough incline at constant speed. The angle of the incline is $$\theta$$ and the coefficient of kinetic friction is $$\mu_k. $$What is the required pulling force parallel to the incline?

$$F = m g (\sin\theta + \mu_k \cos\theta)$$

Question 1

A block of mass $$m$$ rests on an inclined plane with angle $$	heta. $$The coefficient of static friction between the block and the plane is $$\mu_s. $$What is the maximum angle $$	heta_{max}$$ before the block starts to slide?

Accepted Answer

$$	heta_{max} = \arctan(\mu_s)$$

Question 2

A 2 kg object is suspended from a rope and remains at rest. What is the tension in the rope? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$T = 19.6\ \mathrm{N}$$

Question 3

A car of mass $$m = 1000\ \mathrm{kg}$$ accelerates from rest to $$v = 27.8\ \mathrm{m/s} (100 km/h) in$$ $$t = 10\ \mathrm{s}. $$What is the average net force acting on the car?

Accepted Answer

$$F = 2780\ \mathrm{N}$$

Question 4

Which of the following statements about inertial reference frames is correct?

Accepted Answer

The laws of physics are the same in all inertial reference frames.

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

A 5 kg block is pulled across a horizontal surface with a constant velocity. The coefficient of kinetic friction is $$\mu_k = 0.2. $$What is the magnitude of the pulling force?

Accepted Answer

$$F = 0.2 	imes 5 	imes 9.8 = 9.8\ \mathrm{N}$$

Question 8

A steel ball of radius $$R$$ falls through a viscous fluid. According to Stokes' law, what is the magnitude of the drag force acting on the ball at low speeds?

Accepted Answer

$$F = 6 \pi \eta R v$$

Question 9

A block of mass $$m is at $$rest on a horizontal surface. The maximum static friction force before it starts to move is given by:

Accepted Answer

$$f_{s, max} = \mu_s N$$

Question 10

A 0.1 kg steel ball and a 0.1 kg polystyrene ball are dropped from a height of 5 m in air. Neglecting air resistance, which statement is correct?

Accepted Answer

Both balls reach the ground at the same time.

Question 11

A block of mass $$m is at $$rest on a rough incline. Which equation correctly expresses the balance of forces perpendicular to the incline?

Accepted Answer

$$N = mg \cos	heta$$

Question 12

A ball of mass $$m$$ falls through a viscous fluid and quickly reaches terminal velocity $$v_t. $$Which force balance equation is correct at terminal velocity (neglecting buoyancy)?

Accepted Answer

$$mg = 6 \pi \eta R v_t$$

Question 13

Which of the following is NOT a correct statement about friction according to the empirical laws?

Accepted Answer

The kinetic friction coefficient is always greater than the static friction coefficient.

Question 14

A block of mass $$m is $$sliding down a rough incline at constant speed. What is the relationship between the angle $$	heta$$ and the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = 	an	heta$$

Question 15

A mass $$m$$ moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of the net force acting on the mass?

Accepted Answer

$$F = \dfrac{mv^2$}{r}$$

Question 16

A 10 kg box is at rest on a horizontal surface. The coefficient of static friction is $$\mu_s = 0.4. $$What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$F = 39.2\ \mathrm{N}$$

Question 17

Which of the following best describes Newton's third law?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 18

A block of mass $$m is $$pulled up a rough incline at constant speed. The angle of the incline is $$	heta$$ and the coefficient of kinetic friction is $$\mu_k. $$What is the required pulling force parallel to the incline?

Accepted Answer

$$F = m g (\sin	heta + \mu_k \cos	heta)$$

Question 19

A ball is dropped in a viscous fluid and reaches terminal velocity. If the radius of the ball is doubled, what happens to the terminal velocity (assuming Stokes' law applies)?

Accepted Answer

The terminal velocity increases by a factor of 8.

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