Q: For a car traveling at speed $$v$$ around a banked curve of radius $$r$$ with no friction, what is the correct formula for the banking angle $$\theta$$?

$$\tan \theta = \frac{v^2$}{rg}$$

Question 1

A 10 kg box rests on a horizontal floor. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is 0.30. If a horizontal force of 38 N is applied, what is the frictional force acting on the box?

Accepted Answer

$$F_{fr} = 38\ \mathrm{N}$$

Question 2

Which of the following statements about static and kinetic friction is correct?

Accepted Answer

The maximum static friction force is $$F_{fr,\ max} = \mu_s F_N.$$

Question 3

A 0.150 kg ball is swung in a horizontal circle of radius 0.600 m at 2.00 revolutions per second. What is the magnitude of the centripetal force required?

Accepted Answer

$$F = 14.0\ \mathrm{N}$$

Question 4

A car of mass 1000 kg rounds a flat curve of radius 50 m at 15 m/s. If the coefficient of static friction is 0.25, will the car skid? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Yes, because $$F_{fr} \u003c F_{R}$$

Question 5

Which equation correctly relates the period $$T$$ and frequency $$f of an $$object in uniform circular motion?

Accepted Answer

$$T = \frac{1}{f}$$

Question 6

A box sits on an inclined plane and just begins to slide when the angle is increased. Which of the following best explains why?

Accepted Answer

The component of gravity parallel to the plane increases and the normal force decreases.

Question 7

A 10 kg box is pulled along a horizontal surface by a force of 40 N at a $$30^\circ$$ angle above the horizontal. The coefficient of kinetic friction is 0.30. What is the acceleration of the box?

Accepted Answer

$$a = 1.1\ \mathrm{m/s^2$}$$

Question 8

For a car traveling at speed $$v$$ around a banked curve of radius $$r$$ with no friction, what is the correct formula for the banking angle $$	heta$$?

Accepted Answer

$$	an 	heta = \frac{v^2$}{rg}$$

Question 9

A 0.150 kg ball is swung in a vertical circle of radius 1.10 m. What is the minimum speed at the top of the circle to keep the string taut?

Accepted Answer

$$v_{min} = 3.28\ \mathrm{m/s}$$

Question 10

A block of mass $$m$$ slides down an incline at constant speed. If a block of mass $$2m is $$placed on the same incline with the same coefficient of friction, what will happen?

Accepted Answer

It will slide down at constant speed.

Question 11

Which of the following best describes the direction of the acceleration vector for an object in uniform circular motion?

Accepted Answer

It is perpendicular to the velocity and points toward the center.

Question 12

A 5 kg box (A) is connected by a cord over a pulley to a 2 kg box (B) hanging off the edge. The coefficient of kinetic friction between box A and the table is 0.20. What is the acceleration of the system?

Accepted Answer

$$a = 1.4\ \mathrm{m/s^2$}$$

Question 13

Which of the following is true about the force of friction when pulling versus pushing an object at an angle $$	heta$$ above the horizontal?

Accepted Answer

Pulling decreases the normal force and friction.

Question 14

A race car starts from rest and accelerates uniformly to 35 m/s in 11 s on a circular track of radius 250 m. What is the tangential acceleration?

Accepted Answer

$$a_{tan} = 3.2\ \mathrm{m/s^2$}$$

Question 15

Which of the following is NOT a correct statement about friction?

Accepted Answer

Kinetic friction acts when two surfaces are at rest relative to each other.

Question 16

A 10 kg box rests on a 37° incline. It is connected by a cord over a pulley to a hanging mass $$m_B. If$$ $$\mu_s = 0.40$$, what is the minimum value of $$m_B to $$prevent the box from sliding down?

Accepted Answer

$$m_B = 2.8\ \mathrm{kg}$$

Question 17

Which of the following best describes the net force required for uniform circular motion?

Accepted Answer

It is equal to $$m a_R = m \frac{v^2$}{r}$$ and points toward the center.

Question 18

If the radius of a circle is doubled but the period of revolution remains the same, how does the centripetal acceleration change?

Accepted Answer

It is doubled.

Friction and Circular Motion: Physics Study Notes

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