Question 1

A 10-kg mass slides down a frictionless hill inclined at $$10^\circ to $$the horizontal. What is the magnitude of the resultant force acting on the mass?

Accepted Answer

$$17\ \mathrm{N}$$

Question 2

Police find 90.0 m long skid marks at a traffic accident. If the coefficient of friction between the tires and the road is $$\mu = 0.500$$, what was the car's speed when the brakes were applied?

Accepted Answer

$$21.0\ \mathrm{m/s}$$

Question 3

A 30-ton truck collides with a 1000-lb car. During the collision, which statement is correct according to Newton's Third Law?

Accepted Answer

The force on the truck due to the collision is exactly equal to the force on the car.

Question 4

Does the centripetal force acting on an object in uniform circular motion do work on the object?

Accepted Answer

No, because the force and the displacement of the object are perpendicular.

Question 5

A mass $$m$$ slides down a rough $$30^\circ$$ inclined plane with a coefficient of kinetic friction $$\mu_k = 0.20. $$What is the acceleration $$a of $$the mass?

Accepted Answer

$$a = g\sin 30^\circ - \mu_k g\cos 30^\circ$$

Question 6

A $$0.05\ \mathrm{kg}$$ leaf falls $$15\ \mathrm{m}$$ and lands with a speed of $$5\ \mathrm{m/s}. $$What is the work done by air resistance?

Accepted Answer

$$W = mgh - \frac{1}{2}mv^2$

Question 7

Refer to the Atwood machine shown (see $$image_1). If$$ $$M = 10\ \mathrm{kg}$$ and $$m = 5\ \mathrm{kg}$$, what is the acceleration $$a of $$the system? (Neglect friction and pulley mass.)

Accepted Answer

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

Question 8

In the Atwood machine ($$image_1$$), what is the tension $$T in $$the string?

Accepted Answer

$$T = \frac{2Mm}{M+m}g$$

Question 9

A $$1.5\ \mathrm{kg}$$ block is held against a spring by a $$100\ \mathrm{N}$$ force (see $$image_2). $$When released, the block is projected with $$v_1 = 1.0$$\ \mathrm{m/s}$$. What is the spring constant k$ if the spring was compressed by x$ meters?

Accepted Answer

$$k = \frac{F}{x}$$

Question 10

In the scenario of $$image_2$$, the block moves from B to C (rough section, $$\mu_k = 0.2) $$and slows from $$v_2 to$$ $$v_3. If $$the distance is $$S$$, what is the work done by friction?

Accepted Answer

$$W = -\mu_k mg S$$

Question 11

A block slides down a frictionless ramp of height $$h$$ and then across a rough surface ($$\mu_k = 0.2) $$until it stops. If the block's mass is $$m$$, what is the total distance it travels on the rough surface before stopping?

Accepted Answer

$$d = \frac{2h}{\mu_k g}$$

Question 12

A block of mass $$m is $$projected with velocity $$v_1$$ from a compressed spring and moves up a frictionless ramp of height $$h. $$What is the minimum spring compression $$x$$ required if the spring constant is $$k$$?

Accepted Answer

$$\frac{1}{2}kx^2$ = mgh + \frac{1}{2}mv_1$^2$$

Question 13

A leaf falls $$15\ \mathrm{m}$$ and lands at $$5\ \mathrm{m/s}. If $$there were no air resistance, what would be its speed on impact?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 14

A block slides down a $$10\ \mathrm{m}$$ long $$30^\circ$$ incline with $$\mu_k = 0.2$$ starting from rest. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2aL}$$,\ a = g\sin 30^\circ - \mu_k g\cos 30^\circ$

Question 15

Which of the following best describes the energy transformation as a block moves from A to D in $$image_2$$?

Accepted Answer

Elastic potential energy to kinetic energy to gravitational potential energy to thermal energy.

Physics with Calculus: Forces, Energy, and Motion – Step-by-Step Guidance

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