Question 1

Which of the following best describes Newton's First Law of Motion?

Accepted Answer

An object will remain at rest or move with constant velocity unless acted upon by a net external force.

Question 2

A 4 kg crate on a frictionless surface is acted on by two forces: $$\vec{F}_1 = 2\hat{i} + 4\hat{j} N $$and $$\vec{F}_2 = -5\hat{i} + 1\hat{j} N. If $$the crate moves at constant velocity, what is the third force $$\vec{F}_3 in $$unit vector notation?

Accepted Answer

$$\vec{F}_3 = 3\hat{i} - 5\hat{j} N$$

Question 3

A skier of mass 65 kg descends a frictionless slope at $$32^\circ to $$the horizontal. What is the magnitude of the normal force exerted by the slope on the skier?

Accepted Answer

$$n = mg \cos 32^\circ$$

Question 4

A 25 kg box rests on a ramp inclined at angle $$\alpha to $$the horizontal. The coefficient of static friction is $$\mu_s = 0.35. $$What is the minimum angle $$\alpha at $$which the box will start to slide?

Accepted Answer

$$	an \alpha = \mu_s$$

Question 5

A crate of mass 50 kg is pulled by a rope at $$30^\circ$$ above the horizontal with a tension of 250 N. The coefficient of kinetic friction is $$\mu_k = 0.4. $$What is the acceleration of the crate?

Accepted Answer

$$a = \frac{T \cos 30^\circ - \mu_k n}{m}$$

Question 6

A ball of mass $$m is $$dropped into a fluid and experiences a drag force $$f = kv. $$What is the terminal speed $$v_t of $$the ball?

Accepted Answer

$$v_t = \frac{mg}{k}$$

Question 7

A car of mass $$m$$ rounds a frictionless banked curve of radius $$R at $$angle $$	heta to $$the horizontal. What is the speed $$v$$ required to make the turn without sliding?

Accepted Answer

$$v = \sqrt{gR 	an 	heta}$$

Question 8

A small button is placed on a rotating platform of radius $$R = 0.32 m$$, rotating at $$40$$ rev/min. What is the minimum coefficient of static friction $$\mu_s$$ required to prevent the button from sliding off?

Accepted Answer

$$\mu_s = \frac{v^2$}{gR}$$

Question 9

A block of mass $$m is $$attached to a cable and slides down a frictionless hill at angle $$	heta$$ with constant speed. Which statement about the normal force $$n is $$correct?

Accepted Answer

$$n = mg \cos 	heta$$

Question 10

A person pushes a block of mass 10 kg with a force of 50 N at $$30^\circ$$ below the horizontal. The coefficient of static friction is $$\mu_s = 0.5. $$What is the maximum possible static friction force?

Accepted Answer

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

Question 11

A toboggan of mass $$m$$ slides down a hill inclined at angle $$\alpha$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration $$a of $$the toboggan?

Accepted Answer

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

Question 12

A ball of mass $$m$$ moves in a horizontal circle of radius $$R at $$constant speed $$v. $$What is the magnitude of the centripetal force required?

Accepted Answer

$$F_c = \frac{mv^2$}{R}$$

Question 13

A food tray of mass 1.0 kg pushes a milk carton of mass 0.5 kg on a frictionless surface. If the total force applied to the tray is 9.0 N, what is the acceleration of the system?

Accepted Answer

$$a = \frac{9.0}{1.5} m/s$^2$$

Question 14

An elevator of mass 800 kg is moving downward at 10 m/s and slows to a stop over 25 m. What is the tension $$T in $$the supporting cable while the elevator is being brought to rest?

Accepted Answer

$$T = m(g + a_y)$$

Question 15

A glider of mass $$m_1 is $$connected to a hanging mass $$m_2 by a $$massless string over a frictionless pulley. What is the acceleration $$a of $$the system?

Accepted Answer

$$a = \frac{m_2$ g}{m_1$ + m_2$}$$

Question 16

A ball attached to a wire of length $$L$$ moves in a horizontal circle of radius $$R at $$constant speed, making an angle $$	heta$$ with the vertical. What is the tension $$T in $$the wire?

Accepted Answer

$$T = \frac{mg}{\cos 	heta}$$

Question 17

A Ferris wheel rotates at constant speed. At the lowest point of the ride, how does the normal force on a passenger compare to their weight?

Accepted Answer

The normal force is greater than the passenger's weight.

Question 18

A sled moves in a circle of radius $$R on $$frictionless ice, attached by a rope to a fixed post. If the rope breaks, what path will the sled follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point where the rope breaks.

CH5-Newton's Laws of Motion: Equilibrium, Forces, and FBD - EXAM 2

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