Q: A block slides down a rough incline (3-4-5 triangle) starting from rest and travels 5 m down the incline in 2 s. What is the correct expression for the coefficient of kinetic friction $$\mu_k$$?

$$\mu_k = \frac{a_x + g \sin \theta}{g \cos \theta}$$

Q: In a system with two masses $$m_1$$ and $$m_2$$ connected by a string over a pulley (with $$m_1 on a $$rough incline and $$m_2$$ hanging), which equation gives the acceleration $$a_x of $$the system?

$$a_x = \frac{g(m_2$ - \mu_k m_1$ \cos \theta - m_1$ \sin \theta)}{m_1$ + m_2$}$$

Q: A 'massless' rope connects three blocks of mass $$m$$ each, pulled by a force $$F_A at an $$angle $$\theta to $$the horizontal. What is the tension $$T_1 in $$the leftmost rope segment?

$$T_1$$ = \frac{F_A \cos \theta}{3}$$

Q: A helicopter tows a mass $$m at $$constant speed $$v$$ with the cable at angle $$\theta$$ from vertical. If the drag force is $$F_D = \frac{1}{2} \rho A D v^2$, what is the correct expression for the drag coefficient D$?

$$D = \frac{2mg \tan \theta}{\rho A v^2$}$$

Q: A car rounds a banked curve (3-4-5 triangle) with static friction $$\mu_s. $$What is the correct formula for the maximum speed $$v$$ before sliding down the bank?

$$v = \sqrt{r g \frac{\sin \theta + \mu_s \cos \theta}{\cos \theta - \mu_s \sin \theta}}$$

Question 1

A block of mass $$m$$ rests on a horizontal surface. You gradually increase the applied horizontal force $$F_A$$ until the block just begins to move. Which equation correctly describes the maximum static friction force at this point?

Accepted Answer

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

Question 2

A car of mass $$m is $$sliding to a stop on a flat road with a coefficient of kinetic friction $$\mu_k. If $$its initial velocity is $$v_{xi}$$, what is the time $$\Delta t it $$takes to come to a complete stop?

Accepted Answer

$$\Delta t = \frac{v_{xi}}{\mu_k g}$$

Question 3

A block slides down a rough incline (3-4-5 triangle) starting from rest and travels 5 m down the incline in 2 s. What is the correct expression for the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = \frac{a_x + g \sin 	heta}{g \cos 	heta}$$

Question 4

In a system with two masses $$m_1$$ and $$m_2$$ connected by a string over a pulley (with $$m_1 on a $$rough incline and $$m_2$$ hanging), which equation gives the acceleration $$a_x of $$the system?

Accepted Answer

$$a_x = \frac{g(m_2$ - \mu_k m_1$ \cos 	heta - m_1$ \sin 	heta)}{m_1$ + m_2$}$$

Question 5

A 'massless' rope connects three blocks of mass $$m$$ each, pulled by a force $$F_A at an $$angle $$	heta to $$the horizontal. What is the tension $$T_1 in $$the leftmost rope segment?

Accepted Answer

$$T_1$$ = \frac{F_A \cos 	heta}{3}$$

Question 6

A heavy rope of mass $$m is $$attached to a block of mass $$M$$ and pulled with force $$F_A. $$What is the tension $$T_1 at $$the point where the rope meets the block?

Accepted Answer

$$T_1$$ = \frac{M F_A}{M + m}$$

Question 7

A skydiver of mass $$m$$ reaches terminal velocity while falling. Which equation gives the terminal speed $$v in $$terms of air density $$\rho$$, area $$A$$, and drag coefficient $$D$$?

Accepted Answer

$$v = \sqrt{\frac{2mg}{\rho A D}}$$

Question 8

A helicopter tows a mass $$m at $$constant speed $$v$$ with the cable at angle $$	heta$$ from vertical. If the drag force is $$F_D = \frac{1}{2} ho A D v^2$, what is the correct expression for the drag coefficient D$?

Accepted Answer

$$D = \frac{2mg 	an 	heta}{ho A v^2$}$$

Question 9

A car of mass $$m$$ rounds a flat curve of radius $$R$$ with coefficient of static friction $$\mu_s. $$What is the maximum speed $$v$$ before the car starts to slide?

Accepted Answer

$$v = \sqrt{\mu_s g R}$$

Question 10

A car travels around a frictionless banked curve of radius $$r at $$angle $$	heta. $$What is the speed $$v$$ required to avoid slipping up or down the bank?

Accepted Answer

$$v = \sqrt{g r 	an 	heta}$$

Question 11

A car rounds a banked curve (3-4-5 triangle) with static friction $$\mu_s. $$What is the correct formula for the maximum speed $$v$$ before sliding down the bank?

Accepted Answer

$$v = \sqrt{r g \frac{\sin 	heta + \mu_s \cos 	heta}{\cos 	heta - \mu_s \sin 	heta}}$$

Question 12

A bucket of water is spun in a vertical circle of radius $$r. $$What is the minimum speed $$v at $$the top of the circle to prevent the water from falling out?

Accepted Answer

$$v = \sqrt{g r}$$

Question 13

A rollercoaster car of mass $$m$$ moves through a vertical loop of radius $$r at $$speed $$v. $$What is the normal force $$n_1 on $$the car at the top of the loop?

Accepted Answer

$$n_1 = m$$ \frac{$$v^2$$}{r} - m g$$

Question 14

A wheel of radius $$r$$ rotates with initial angular speed $$\omega_i$$ and constant angular acceleration $$\alpha$$ until it stops. How many rotations $$N$$ does it make before stopping?

Accepted Answer

$$N = -\frac{\omega_i^2$}{4 \pi \alpha}$$

Question 15

Which of the following statements about drag force is correct?

Accepted Answer

Drag force increases with the square of the object's speed.

Question 16

A mass $$m is $$spun in a horizontal circle of radius $$r at $$constant speed $$v$$ using a string. What is the correct expression for the required centripetal acceleration?

Accepted Answer

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

Question 17

A mass $$m_2 is $$spun in a horizontal circle at the end of a string of length $$l$$, with another mass $$m_1$$ hanging vertically. What is the angular speed $$\omega$$ required to keep $$m_1$$ stationary?

Accepted Answer

$$\omega = \sqrt{\frac{m_1$ g}{m_2$ l}}$$

Applications of Newton’s Laws: Friction, Tension, Drag, and Circular Motion

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