Q: Which equation best describes the acceleration of a block sliding down an inclined plane with friction?

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

Q: A skier is on a $$15^\circ$$ slope with $$\mu_k = 0.15. $$What is the net force acting on a $$70 \ \mathrm{kg}$$ skier?

$$F_{net} = 70 \times 9.8 \times (\sin 15^\circ - 0.15 \cos 15^\circ)$$

Question 1

A 10 kg block and a 5 kg block are connected by a string over a frictionless, massless pulley. What is the acceleration of the 10 kg block? (Assume $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$a = 3.27 \ \mathrm{m/s^2$}$$

Question 2

What is the tension in the string connecting the 10 kg and 5 kg blocks in the pulley system described above?

Accepted Answer

$$T = 65.3 \ \mathrm{N}$$

Question 3

Mary is heading out for a cup of coffee. The elevator is moving downward and approaching the first floor (slowing down) at a rate of $$2 \ \mathrm{m/s^2$}. If $$Mary has a mass of $$60 \ \mathrm{kg}$$, what is the reading on the scale in the elevator?

Accepted Answer

$$W = 672 \ \mathrm{N}$$

Question 4

A box is sliding down a $$30^\circ$$ slope where the coefficient of friction is $$\mu_k = 0.15. $$How fast will the box be going $$5 \ \mathrm{s}$$ after it starts sliding?

Accepted Answer

$$v = 16.1 \ \mathrm{m/s}$$

Question 5

A car of mass $$1500 \ \mathrm{kg}$$ and $$v_0 = 30$$ \ \mathrm{m/s}$$ is on a dry road with $$\mu_k = 0.8$$. How far will the car travel if the wheels lock up (i.e., skid) and the car slides to a stop?

Accepted Answer

$$d = 71.6 \ \mathrm{m}$$

Question 6

How far will the car travel if the ABS system kicks in ($$\mu_s = 0.9) $$and the car slows down at the maximum rate without the wheels locking up?

Accepted Answer

$$d = 50.8 \ \mathrm{m}$$

Question 7

How much force does the homeowner need to exert to push the lawnmower across the lawn at constant velocity if the coefficient of friction is $$\mu = 0.25$$ and the pushing force is directed at an angle of $$25^\circ$$ below the horizontal?

Accepted Answer

$$F = 220 \ \mathrm{N}$$

Question 8

A skier is on a $$15^\circ$$ slope where the coefficient of friction is $$\mu_k = 0.15. $$How fast will they be going $$5 \ \mathrm{s}$$ after starting from rest?

Accepted Answer

$$v = 10.2 \ \mathrm{m/s}$$

Question 9

Which equation best describes the acceleration of a block sliding down an inclined plane with friction?

Accepted Answer

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

Question 10

If a car of mass $$m is $$traveling at velocity $$v_0$$ and comes to a stop due to kinetic friction $$\mu_k$$, what is the stopping distance $$d$$?

Accepted Answer

$$d = \frac{v_0$^2}{2 \mu_k g}$$

Question 11

A block of mass $$m is $$pulled up a frictionless incline at angle $$	heta$$ with constant velocity. What is the minimum force required?

Accepted Answer

$$F = m g \sin 	heta$$

Question 12

A $$5 \ \mathrm{kg}$$ block is pulled up a $$30^\circ$$ incline with a coefficient of kinetic friction $$\mu_k = 0.2 at $$constant velocity. What is the tension in the rope?

Accepted Answer

$$T = 34.3 \ \mathrm{N}$$

Question 13

If the elevator in question 3 is accelerating upward at $$2 \ \mathrm{m/s^2$}$$, what is the reading on the scale for Mary?

Accepted Answer

$$W = 720 \ \mathrm{N}$$

Question 14

A $$10 \ \mathrm{kg}$$ block is connected to a $$5 \ \mathrm{kg}$$ block over a frictionless pulley. If the system starts from rest, what is the velocity of the blocks after $$2 \ \mathrm{s}$$?

Accepted Answer

$$v = 6.54 \ \mathrm{m/s}$$

Question 15

A skier is on a $$15^\circ$$ slope with $$\mu_k = 0.15. $$What is the net force acting on a $$70 \ \mathrm{kg}$$ skier?

Accepted Answer

$$F_{net} = 70 	imes 9.8 	imes (\sin 15^\circ - 0.15 \cos 15^\circ)$$

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