Q: A car of mass $$m$$ rounds a frictionless banked curve of radius $$R at $$speed $$v. $$What is the correct expression for the net force required to keep the car in circular motion?

$$F_{\text{net}} = \frac{m v^2$}{R}$$

Q: A car of mass $$m$$ rounds a banked curve of radius $$R at $$speed $$v$$ with no friction. What is the correct formula for the banking angle $$\theta$$ required for the car to make the turn?

$$\tan \theta = \frac{v^2$}{g R}$$

Question 1

A car of mass $$m is at $$rest on a flat road. According to Newton's first law, which of the following must be true about the forces acting on the car?

Accepted Answer

The sum of all forces acting on the car is zero: $$\sum \vec{F} = 0.$$

Question 2

A box of mass $$m is $$pulled horizontally across a rough surface at constant velocity. Which equation correctly describes the relationship between the applied force $$F_{	ext{app}}$$ and the friction force $$f_k$$?

Accepted Answer

$$F_{	ext{app}} = f_k$$

Question 3

Which of the following statements about free-body diagrams is correct?

Accepted Answer

The term $$m a$$ should not be included in a free-body diagram.

Question 4

A block of mass $$m$$ sits on a horizontal surface. If the coefficient of static friction is $$\mu_s$$, what is the maximum possible static friction force before the block begins to slide?

Accepted Answer

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

Question 5

A car of mass $$m$$ rounds a frictionless banked curve of radius $$R at $$speed $$v. $$What is the correct expression for the net force required to keep the car in circular motion?

Accepted Answer

$$F_{	ext{net}} = \frac{m v^2$}{R}$$

Question 6

A person pushes a box across a floor. The box starts to move only after the applied force exceeds a certain value. Which physical concept explains this behavior?

Accepted Answer

Static friction must be overcome.

Question 7

A block is sliding at constant speed on a horizontal surface. If the coefficient of kinetic friction is $$\mu_k$$ and the normal force is $$n$$, what is the magnitude of the friction force?

Accepted Answer

$$f_k = \mu_k n$$

Question 8

Which of the following best describes the direction of the friction force acting on an object sliding on a surface?

Accepted Answer

Parallel to the surface and opposite to the direction of motion

Question 9

A ball attached to a string moves in a horizontal circle. If the string suddenly breaks, what path will the ball follow?

Accepted Answer

It will move in a straight line tangent to the circle at the point of release.

Question 10

Which of the following is NOT a correct step in the problem-solving strategy for equilibrium situations?

Accepted Answer

Include $$m a as a $$force in the free-body diagram.

Question 11

A block of mass $$m is $$pulled by a force $$F at an $$angle $$	heta$$ above the horizontal across a rough surface. The coefficient of kinetic friction is $$\mu_k. $$What is the correct expression for the normal force $$n$$ acting on the block?

Accepted Answer

$$n = m g - F \sin 	heta$$

Question 12

Which of the following statements about 'centrifugal force' is correct according to the study materials?

Accepted Answer

There is no such thing as centrifugal force in an inertial frame of reference.

Question 13

A windshield wiper squeaks on dry glass but not on wet glass. What physical principle explains this phenomenon?

Accepted Answer

Static friction is higher on dry glass, causing stick-slip motion.

Question 14

A block of mass $$m is at $$rest on a horizontal surface. A horizontal force $$F is $$applied, but the block does not move. Which inequality must be satisfied?

Accepted Answer

$$F \u003c \mu_s n$$

Question 15

A car of mass $$m$$ rounds a banked curve of radius $$R at $$speed $$v$$ with no friction. What is the correct formula for the banking angle $$	heta$$ required for the car to make the turn?

Accepted Answer

$$	an 	heta = \frac{v^2$}{g R}$$

Question 16

Which of the following is the correct expression for the net force acting on a particle in uniform circular motion?

Accepted Answer

$$F_{	ext{net}} = \frac{m v^2$}{R}$$

Question 17

A block of mass $$m is $$sliding down an inclined plane with angle $$	heta$$ and coefficient of kinetic friction $$\mu_k. $$What is the correct expression for the friction force?

Accepted Answer

$$f_k = \mu_k m g \cos 	heta$$

Question 18

Which of the following is a correct statement about the relationship between static and kinetic friction?

Accepted Answer

The coefficient of static friction is usually greater than the coefficient of kinetic friction.

Question 19

A block of mass $$m is $$connected to another block of mass $$M by a $$rope over a frictionless pulley. If $$m is on a $$horizontal surface with coefficient of kinetic friction $$\mu_k$$, what is the acceleration of the system?

Accepted Answer

$$a = \frac{M g - \mu_k m g}{m + M}$$

Applying Newton's Laws: Equilibrium, Dynamics, Friction, and Circular Motion

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