Q: Which of the following is the correct SI unit and dimension for energy?

$$\text{Joule (J)},\ [M][L]^2/[T]^2$$

Q: A car travels 100 m east in 10 s, then 50 m west in 5 s. What is the average velocity for the entire trip?

$$\frac{100\ \text{m} - 50\ \text{m}}{10\ \text{s} + 5\ \text{s}} = \frac{50}{15} = 3.33\ \text{m/s}$$\ east

Q: A block of mass $$m$$ slides up a frictionless ramp with initial velocity $$v_0$$ and comes to rest after traveling a distance $$d up $$the incline. What is the angle $$\theta of $$the ramp if $$d = \frac{v_0$^2}{2g\sin\theta}$$?

$$\sin\theta = \frac{v_0$^2}{2gd}$$

Q: A 10 kg box is pulled across a horizontal surface with a constant velocity by a force of 40 N. What is the coefficient of kinetic friction between the box and the surface? (Assume $$g = 10\ \text{m/s}^2)$$

$$\mu_k = \frac{F}{mg} = \frac{40}{10 \times 10} = 0.4$$

Q: A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude and direction of $$\vec{A}$$?

$$|\vec{A}| = 5,\ \theta = \tan$$^{-1}$$\left(\frac{4}{3}\right)$$

Q: A 5 kg block is at rest on a frictionless horizontal surface. A force of 20 N is applied to the block. What is the acceleration of the block?

$$a = \frac{F}{m} = \frac{20}{5} = 4\ \text{m/s}^2$$

Q: A 10 kg box is at rest on a ramp inclined at $$30^\circ to $$the horizontal. The coefficient of static friction is $$\mu_s = 0.5. $$What is the maximum force of static friction?

$$f_{s,\text{max}} = \mu_s N = 0.5 \times 10 \times 9.8 \times \cos 30^\circ$$

Q: A 15 kg box is in an elevator accelerating upward at $$2\ \text{m/s}^2. $$What is the apparent weight of the box? ($$g = 10\ \text{m/s}^2)$$

$$W_{\text{apparent}} = m(g + a) = 15 \times (10 + 2) = 180\ \text{N}$$

Question 1

Which of the following is the correct SI unit and dimension for energy?

Accepted Answer

$$	ext{Joule (J)},\ [M][L]^2/[T]^2$$

Question 2

A car travels 100 m east in 10 s, then 50 m west in 5 s. What is the average velocity for the entire trip?

Accepted Answer

$$\frac{100\ 	ext{m} - 50\ 	ext{m}}{10\ 	ext{s} + 5\ 	ext{s}} = \frac{50}{15} = 3.33\ 	ext{m/s}$$\ east

Question 3

A projectile is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$What is the time it takes to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 4

A block of mass $$m$$ slides up a frictionless ramp with initial velocity $$v_0$$ and comes to rest after traveling a distance $$d up $$the incline. What is the angle $$	heta of $$the ramp if $$d = \frac{v_0$^2}{2g\sin	heta}$$?

Accepted Answer

$$\sin	heta = \frac{v_0$^2}{2gd}$$

Question 5

Which of the following statements about friction is correct?

Accepted Answer

The force of kinetic friction is independent of the area of contact between surfaces.

Question 6

A 10 kg box is pulled across a horizontal surface with a constant velocity by a force of 40 N. What is the coefficient of kinetic friction between the box and the surface? (Assume $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$\mu_k = \frac{F}{mg} = \frac{40}{10 	imes 10} = 0.4$$

Question 7

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude and direction of $$\vec{A}$$?

Accepted Answer

$$|\vec{A}| = 5,\ 	heta = 	an$$^{-1}$$\left(\frac{4}{3}ight)$$

Question 8

A 2 kg object is acted on by two forces: $$\vec{F}_1 = (3\hat{x} + 4\hat{y}) N $$and $$\vec{F}_2 = (-3\hat{x} + 2\hat{y}) N. $$What is the magnitude of the object's acceleration?

Accepted Answer

$$a = \frac{\sqrt{(3 + (-3))^2$ + (4 + 2)^2$}}{2} = \frac{6}{2} = 3\ 	ext{m/s}^2$$

Question 9

A 5 kg block is at rest on a frictionless horizontal surface. A force of 20 N is applied to the block. What is the acceleration of the block?

Accepted Answer

$$a = \frac{F}{m} = \frac{20}{5} = 4\ 	ext{m/s}^2$$

Question 10

A 10 kg box is at rest on a ramp inclined at $$30^\circ to $$the horizontal. The coefficient of static friction is $$\mu_s = 0.5. $$What is the maximum force of static friction?

Accepted Answer

$$f_{s,	ext{max}} = \mu_s N = 0.5 	imes 10 	imes 9.8 	imes \cos 30^\circ$$

Question 11

A 15 kg box is in an elevator accelerating upward at $$2\ 	ext{m/s}^2. $$What is the apparent weight of the box? ($$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$W_{	ext{apparent}} = m(g + a) = 15 	imes (10 + 2) = 180\ 	ext{N}$$

Question 12

A ball is thrown straight up with initial velocity $$v_0. At $$the peak of its trajectory, what are the velocity and acceleration?

Accepted Answer

$$v = 0,\ a = -g$$

Question 13

A 2 kg object is attached to a rope and hangs at rest from the ceiling. What is the tension in the rope?

Accepted Answer

$$T = mg = 2 	imes 9.8 = 19.6\ 	ext{N}$$

Question 14

A car of mass $$m is $$moving in a circle of radius $$r at $$constant speed $$v. $$What is the direction of the net force acting on the car?

Accepted Answer

Toward the center of the circle

Question 15

A 1 kg object is acted on by a net force of $$\vec{F} = (6\hat{x} + 8\hat{y}) N. $$What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{\sqrt{6^2$ + 8^2$}}{1} = 10\ 	ext{m/s}^2$$

Question 16

A 3 kg block is connected by a string over a frictionless pulley to a 2 kg block hanging vertically. If the system is released from rest, what is the acceleration of the system? (Assume $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$a = \frac{2 	imes 10}{3 + 2} = 4\ 	ext{m/s}^2$$

Physics with Calculus: Foundations, Kinematics, and Newton's Laws

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