Question 1

A small block of mass $$m is $$placed inside an inverted cone that rotates about a vertical axis. The walls of the cone make an angle $$\beta$$ with the horizontal, and the coefficient of static friction between the block and the cone is $$\mu_s. If $$the block is to remain at a constant height $$h$$ above the apex, which of the following forces does NOT act on the block?

Accepted Answer

The tension force

Question 2

When the cone is rotating as slowly as possible (maximum period $$T_{max}$$), what is the direction of the friction force acting on the block?

Accepted Answer

Up along the direction of the cone's inner surface

Question 3

For the rotating cone scenario, what is the radius $$R of $$the circular path that the block follows, in terms of $$h$$ and $$\beta$$?

Accepted Answer

$$R = h 	an \beta$$

Question 4

A box of mass $$m is $$pushed with a force $$F at an $$angle $$	heta$$ below the horizontal and does not move. What is the magnitude of the friction force acting on the box?

Accepted Answer

$$F \cos 	heta$$

Question 5

A boat is tied to three bollards with ropes at angles $$	heta as $$shown. If the forces from ropes 1 and 2 are both $$F$$, what is the magnitude of the force from the third rope to keep the boat in equilibrium?

Accepted Answer

$$2F \cos 	heta$$

Question 6

An object is hanging by a string from the ceiling of an elevator moving upward at constant speed. What is the magnitude of the tension in the string?

Accepted Answer

The magnitude of the tension in the string is equal to the magnitude of the weight of the object.

Question 7

A crate is pulled along a rough horizontal surface by a force $$F at an $$angle, and the crate does not move. What is the maximum possible value of the static friction force?

Accepted Answer

$$\mu_s N$$

Question 8

A skier is heading down a hill with an incline of $$	heta. $$What is the component of the gravitational force accelerating them down the hill?

Accepted Answer

$$mg \sin 	heta$$

Question 9

A small metal cylinder rests on a circular turntable rotating at a constant rate. If the cylinder is moved to a new location twice as far from the center, what happens to its speed and acceleration?

Accepted Answer

Both the speed and the acceleration of the cylinder increase.

Question 10

Which of the following statements about centripetal acceleration is FALSE?

Accepted Answer

If you are in a car turning left, the force you feel pushing you to the right is the force that causes the centripetal acceleration.

Question 11

Two cars, one of mass $$m_1$$ and one of mass $$m_2$$, drive around a curve of radius $$R at $$the same acceleration. How do their speeds compare?

Accepted Answer

Their speeds are equal.

Question 12

A box is pushed with a force $$F at an $$angle $$	heta$$ below the horizontal. What is the normal force $$N$$ acting on the box?

Accepted Answer

$$N = mg + F \sin 	heta$$

Question 13

A crate is pulled with a force $$F$$ and just begins to move. If the coefficient of kinetic friction is $$\mu_k$$, what is the force of kinetic friction acting on the crate?

Accepted Answer

$$\mu_k N$$

Question 14

A mass $$m$$ moves in a circle of radius $$R$$ with constant speed $$v. $$What is the direction of the net force acting on the mass?

Accepted Answer

Toward the center of the circle

Question 15

A box is pushed but does not move. Which statement about the friction force is correct?

Accepted Answer

The friction force is equal in magnitude to the applied force, up to a maximum of $$\mu_s N.$$

Question 16

A mass $$m is $$attached to a string and swung in a horizontal circle of radius $$R at $$constant speed $$v. $$What is the magnitude of the acceleration?

Accepted Answer

$$\frac{v^2$}{R}$$

Question 17

A crate is pulled with a force $$F$$ and does not move. If the maximum static friction force is $$15\ \mathrm{N}$$, what is the static friction force when $$F = 10\ \mathrm{N}$$?

Accepted Answer

$$10\ \mathrm{N}$$

Question 18

You feel heavier in an elevator if you are:

Accepted Answer

Accelerating up

Physics with Calculus: Newton's Laws, Friction, Circular Motion, and Proportional Reasoning

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