Q: A car traveling at 20 m/s comes to a stop in a distance of 50 m. Assuming constant deceleration, what is the magnitude of the car's acceleration?

$$a = -4.0 \\ \mathrm{m/s^2$}$$

Q: If the coefficient of friction between a passenger and the seat is $$\mu = 0.3$$, what is the maximum frictional force that can act on a 70 kg passenger?

$$F_{\text{friction}} = 206 \\ \mathrm{N}$$

Q: A block A of mass $$m_A$$ sits on a $$20^\\circ$$ ramp with $$\mu_s = 0.3. $$What is the minimum value of $$m_B ($$block B) required so that both blocks slide down the ramp, if $$m_A = 10 kg $$and block B is frictionless?

$$m_B \u003e m_A (\sin 20^\\circ - \mu_s \cos 20^\\circ)$$

Q: If the coefficient of static friction between block A and the ramp is $$\mu_s = 0.3$$, and the ramp angle is $$20^\\circ$$, what is the minimum force required to start moving block A up the ramp?

$$F = m_A g (\sin 20^\\circ + 0.3 \cos 20^\\circ)$$

Question 1

A car traveling at 20 m/s comes to a stop in a distance of 50 m. Assuming constant deceleration, what is the magnitude of the car's acceleration?

Accepted Answer

$$a = -4.0 \ \mathrm{m/s^2$}$$

Question 2

Given the car in the previous question, what is the net force acting on a 70 kg passenger during the deceleration?

Accepted Answer

$$F = 280 \ \mathrm{N}$$

Question 3

If the coefficient of friction between a passenger and the seat is $$\mu = 0.3$$, what is the maximum frictional force that can act on a 70 kg passenger?

Accepted Answer

$$F_{	ext{friction}} = 206 \ \mathrm{N}$$

Question 4

Will a 70 kg passenger slide forward if not wearing a seatbelt, given the car's deceleration and $$\mu = 0.3$$ between the passenger and the seat?

Accepted Answer

Yes, because the required force to stop the passenger exceeds the maximum frictional force.

Question 5

Which of the following equations correctly relates final velocity, initial velocity, acceleration, and displacement for constant acceleration?

Accepted Answer

$$v_f^2$ = v_i^2$ + 2a(x_f - x_i)$$

Question 6

A block A of mass $$m_A$$ sits on a $$20^\circ$$ ramp with $$\mu_s = 0.3. $$What is the minimum value of $$m_B ($$block B) required so that both blocks slide down the ramp, if $$m_A = 10 kg $$and block B is frictionless?

Accepted Answer

$$m_B \u003e m_A (\sin 20^\circ - \mu_s \cos 20^\circ)$$

Question 7

For block A on the ramp, which force acts perpendicular to the surface?

Accepted Answer

Normal force

Question 8

If block A does not slide when $$m_B = 0$$, what does this indicate about the relationship between the frictional force and the component of gravity parallel to the ramp?

Accepted Answer

The frictional force is greater than or equal to the parallel component of gravity.

Question 9

Which of the following best describes the role of the coefficient of friction $$\mu in $$determining whether an object slides down an inclined plane?

Accepted Answer

$$\mu$$ determines the maximum static friction force that can oppose motion.

Question 10

A block of mass $$m is $$placed on a frictionless incline of angle $$	heta. $$What is the acceleration of the block down the incline?

Accepted Answer

$$a = g \sin 	heta$$

Question 11

If the coefficient of static friction between block A and the ramp is $$\mu_s = 0.3$$, and the ramp angle is $$20^\circ$$, what is the minimum force required to start moving block A up the ramp?

Accepted Answer

$$F = m_A g (\sin 20^\circ + 0.3 \cos 20^\circ)$$

Question 12

Which equation would you use to find the time it takes for a car to stop, given initial velocity $$v_i$$, final velocity $$v_f = 0$$, and constant acceleration $$a$$?

Accepted Answer

$$t = \frac{v_f - v_i}{a}$$

Question 13

A block of mass $$m is at $$rest on a ramp. What is the condition for the block to remain at rest in terms of the coefficient of static friction $$\mu_s$$ and the ramp angle $$	heta$$?

Accepted Answer

$$\mu_s \geq 	an 	heta$$

Question 14

If block B is coated to be frictionless, what forces act on block B as it slides down the ramp?

Accepted Answer

Gravity and normal force

Question 15

A car decelerates at $$a = -4.0 \ \mathrm{m/s^2$}$$ from $$v_i = 20 \ \mathrm{m/s} to $$rest. How long does it take to stop?

Accepted Answer

$$t = 5 \ \mathrm{s}$$

Question 16

Which of the following is NOT a correct kinematic equation for constant acceleration?

Accepted Answer

$$x_f = x_i + v_f t + \frac{1}{2} a t^2$

Kinematics and Dynamics: Friction, Inclined Planes, and Motion with Constant Acceleration

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