Q: For an object on a rough inclined plane, the critical angle $$\theta_{crit,s} at $$which the object just begins to slide is related to the coefficient of static friction $$\mu_s by $$which equation?

$$\theta_{crit,s} = \arctan(\mu_s)$$

Question 1

According to Newton's Third Law, when you push a 40 kg ice block on a frictionless frozen lake with a force of 20 N, what is the force that the block exerts on you?

Accepted Answer

$$20\ \mathrm{N}$$

Question 2

Which of the following is NOT an action-reaction pair according to Newton's Third Law?

Accepted Answer

Weight of the book & normal force on the book

Question 3

Two blocks of mass $$3\ \mathrm{kg}$$ and $$5\ \mathrm{kg}$$ are connected by a massless string. If you pull the $$5\ \mathrm{kg}$$ block with a constant force of $$30\ \mathrm{N} on a $$frictionless surface, what is the acceleration of the system?

Accepted Answer

$$3.75\ \mathrm{m/s^2$}$$

Question 4

A $$4\ \mathrm{kg}$$ block rests on a frictionless table and is connected to a $$2\ \mathrm{kg}$$ block hanging off the table by a cable and massless pulley. What is the acceleration of the system? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.45\ \mathrm{m/s^2$}$$

Question 5

In an Atwood machine, a $$6\ \mathrm{kg}$$ block and a $$4\ \mathrm{kg}$$ block are connected by a string over a pulley. What is the acceleration of the system? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$1.96\ \mathrm{m/s^2$}$$

Question 6

A $$10\ \mathrm{kg}$$ block is tied via a string to a $$5\ \mathrm{kg}$$ block on a rough table where $$\mu_s = 0.5$$ and $$\mu_k = 0.3. If $$you pull on the $$10\ \mathrm{kg}$$ block with $$90\ \mathrm{N}$$ and the objects start moving, what is the acceleration of the blocks? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.4\ \mathrm{m/s^2$}$$

Question 7

A $$4.0\ \mathrm{kg}$$ box sits on a frictionless inclined plane at $$21^\circ$$ and is held in place by a cord parallel to the plane. What is the tension in the cord? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$14\ \mathrm{N}$$

Question 8

A $$2.0\ \mathrm{kg}$$ block is launched up a $$40^\circ$$ ramp at $$10\ \mathrm{m/s}. If $$the block comes to a stop when it reaches a point $$3\ \mathrm{m}$$ vertically above the bottom of the ramp, what is the coefficient of kinetic friction between the block and the ramp?

Accepted Answer

$$0.51$$

Question 9

A $$3\ \mathrm{kg}$$ block is at rest on an adjustable ramp. When the ramp is tilted to a $$20^\circ$$ angle, the block slides with constant velocity. What is the coefficient of kinetic friction between the ramp and the block?

Accepted Answer

$$\mu_k = 0.36$$

Question 10

A $$5\ \mathrm{kg}$$ block A is placed on a $$10\ \mathrm{kg}$$ block B. Block A is tied to a wall, while Block B is pulled with a force of $$45\ \mathrm{N}$$ and moves to the right. The coefficient of kinetic friction between all surfaces is $$\mu_k = 0.2. $$What is the tension on Block A?

Accepted Answer

$$1.8\ \mathrm{N}$$

Question 11

You push a $$30\ \mathrm{kg}$$ mini-fridge up a $$20^\circ$$ incline. Your push is $$120\ \mathrm{N}$$ angled $$30^\circ$$ above the axis of the incline. If the coefficients of friction between the box and the ramp are $$\mu_s=0.3$$ and $$\mu_k=0.2$$, what is the box's acceleration?

Accepted Answer

$$0\ \mathrm{m/s^2$} (no $$direction)

Question 12

A $$4\ \mathrm{kg}$$ block sits on top of a $$6\ \mathrm{kg}$$ block which is on a frictionless surface. The coefficients of friction between the two blocks are $$\mu_s=0.5$$ and $$\mu_k=0.3. $$What is the maximum force you can pull on the bottom block with so that the objects move together?

Accepted Answer

$$19.6\ \mathrm{N}$$

Question 13

A car is parked on a street that runs down a $$35.0^\circ$$ hill. After a snowstorm, the car just begins to slide. What is the coefficient of static friction between the car tires and the icy road?

Accepted Answer

$$\mu_s = 0.47$$

Question 14

Two blocks, A and B, sit on back-to-back rough inclined planes and are connected by a cable. The angles of the planes are $$	heta_A=15^\circ$$ and $$	heta_B=30^\circ. $$The masses of the blocks are $$m_A=2\ \mathrm{kg}$$ and $$m_B=5\ \mathrm{kg}$$, and $$\mu_k=0.2. $$What is the magnitude of their acceleration?

Accepted Answer

$$1.02\ \mathrm{m/s^2$}$$

Question 15

For an object on a rough inclined plane, the critical angle $$	heta_{crit,s} at $$which the object just begins to slide is related to the coefficient of static friction $$\mu_s by $$which equation?

Accepted Answer

$$	heta_{crit,s} = \arctan(\mu_s)$$

Question 16

When solving for the acceleration of a system of connected objects, what is a useful shortcut?

Accepted Answer

Add all the masses together and treat as a single object, ignoring internal tensions.

Question 17

A $$10\ \mathrm{kg}$$ box rests on a frictionless floor, with a $$5\ \mathrm{kg}$$ box on top of it. The coefficients of friction between the boxes are $$\mu_s = 0.7$$ and $$\mu_k = 0.3. $$What is the maximum acceleration the bottom box can have so that the two boxes move together?

Accepted Answer

$$6.86\ \mathrm{m/s^2$}$$

Question 18

When two blocks are stacked and the bottom block is pulled, what type of friction acts between the blocks if they move together?

Accepted Answer

Static friction

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