Q: A car accelerates from rest to a velocity of $$20\ \text{m/s} in$$ $$5\ \text{s}. $$What is the car's acceleration?

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

Q: A $$10\ \text{kg}$$ box is pulled across a horizontal floor with a force of $$50\ \text{N}. If $$the coefficient of kinetic friction is $$\mu_k = 0.3$$, what is the magnitude of the kinetic friction force?

$$f_k = \mu_k n = 0.3 \times 10 \times 9.8 = 29.4\ \text{N}$$

Q: A $$5\ \text{kg}$$ object is moving at $$10\ \text{m/s}. $$What is its kinetic energy?

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} \times 5 \times 10^2$ = 250\ \text{J}$$

Q: A $$3\ \text{kg}$$ ball is dropped from a height of $$5\ \text{m}. $$What is its potential energy just before it hits the ground?

$$U = m g h = 3 \times 9.8 \times 5 = 147\ \text{J}$$

Q: A $$2\ \text{kg}$$ object is acted upon by a force of $$10\ \text{N}$$ for $$3\ \text{s}. $$What is the impulse delivered to the object?

$$J = F \Delta t = 10 \times 3 = 30\ \text{kg m/s}$$

Q: A $$0.2\ \text{kg}$$ mass is attached to a string and swung in a circle of radius $$0.5\ \text{m} at a $$speed of $$2\ \text{m/s}. $$What is its angular velocity $$\omega$$?

$$\omega = \frac{v}{r} = \frac{2}{0.5} = 4\ \text{rad/s}$$

Q: A $$1\ \text{kg}$$ object is rotating with angular velocity $$\omega = 3\ \text{rad/s}$$ and has a moment of inertia $$I = 2\ \text{kg m}^2. $$What is its rotational kinetic energy?

$$K = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} \times 2 \times 9 = 9\ \text{J}$$

Question 1

A car accelerates from rest to a velocity of $$20\ 	ext{m/s} in$$ $$5\ 	ext{s}. $$What is the car's acceleration?

Accepted Answer

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

Question 2

A $$10\ 	ext{kg}$$ box is pulled across a horizontal floor with a force of $$50\ 	ext{N}. If $$the coefficient of kinetic friction is $$\mu_k = 0.3$$, what is the magnitude of the kinetic friction force?

Accepted Answer

$$f_k = \mu_k n = 0.3 	imes 10 	imes 9.8 = 29.4\ 	ext{N}$$

Question 3

Which of the following best describes the difference between static and kinetic friction?

Accepted Answer

Static friction ($$f_s) $$prevents motion up to a maximum value, while kinetic friction ($$f_k) $$acts when objects are already moving.

Question 4

A $$2\ 	ext{kg}$$ mass is attached to a spring with a spring constant $$k = 100\ 	ext{N/m}. $$What is the period $$T of $$oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{2}{100}} \approx 0.89\ 	ext{s}$$

Question 5

A $$5\ 	ext{kg}$$ object is moving at $$10\ 	ext{m/s}. $$What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 5 	imes 10^2$ = 250\ 	ext{J}$$

Question 6

A $$3\ 	ext{kg}$$ ball is dropped from a height of $$5\ 	ext{m}. $$What is its potential energy just before it hits the ground?

Accepted Answer

$$U = m g h = 3 	imes 9.8 	imes 5 = 147\ 	ext{J}$$

Question 7

A $$0.5\ 	ext{kg}$$ ball moving at $$4\ 	ext{m/s}$$ collides with a stationary $$0.5\ 	ext{kg}$$ ball. After the collision, the first ball stops and the second moves at $$4\ 	ext{m/s}. $$What principle is illustrated?

Accepted Answer

Conservation of momentum ($$p = m v)$$

Question 8

A $$2\ 	ext{kg}$$ object is acted upon by a force of $$10\ 	ext{N}$$ for $$3\ 	ext{s}. $$What is the impulse delivered to the object?

Accepted Answer

$$J = F \Delta t = 10 	imes 3 = 30\ 	ext{kg m/s}$$

Question 9

A $$0.2\ 	ext{kg}$$ mass is attached to a string and swung in a circle of radius $$0.5\ 	ext{m} at a $$speed of $$2\ 	ext{m/s}. $$What is its angular velocity $$\omega$$?

Accepted Answer

$$\omega = \frac{v}{r} = \frac{2}{0.5} = 4\ 	ext{rad/s}$$

Question 10

A $$1\ 	ext{kg}$$ object is rotating with angular velocity $$\omega = 3\ 	ext{rad/s}$$ and has a moment of inertia $$I = 2\ 	ext{kg m}^2. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} 	imes 2 	imes 9 = 9\ 	ext{J}$$

Question 11

A $$0.5\ 	ext{kg}$$ mass is attached to a spring and oscillates with amplitude $$A = 0.2\ 	ext{m}$$ and spring constant $$k = 50\ 	ext{N/m}. $$What is the maximum potential energy stored in the spring?

Accepted Answer

$$U_{max} = \frac{1}{2} k A^2$ = \frac{1}{2} 	imes 50 	imes 0.04 = 1\ 	ext{J}$$

Question 12

A $$60\ 	ext{kg}$$ person stands on a scale in an elevator accelerating upward at $$2\ 	ext{m/s}^2. $$What is the normal force $$n on $$the person?

Accepted Answer

$$n = m (g + a) = 60 	imes (9.8 + 2) = 708\ 	ext{N}$$

Question 13

A $$2\ 	ext{kg}$$ object is moving at $$5\ 	ext{m/s}$$ and comes to rest in $$4\ 	ext{s}$$ due to a constant drag force. What is the magnitude of the drag force?

Accepted Answer

$$D = m a = m \frac{\Delta v}{\Delta t} = 2 	imes \frac{-5}{4} = -2.5\ 	ext{N} ($$magnitude $$2.5\ 	ext{N})$$

Question 14

A $$0.1\ 	ext{kg}$$ pendulum swings with a frequency $$f = 2\ 	ext{Hz}. $$What is its period $$T$$?

Accepted Answer

$$T = \frac{1}{f} = \frac{1}{2} = 0.5\ 	ext{s}$$

Question 15

A $$4\ 	ext{kg}$$ object is subjected to a torque $$	au = 8\ 	ext{Nm}$$ and has a moment of inertia $$I = 2\ 	ext{kg m}^2. $$What is its angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{	au}{I} = \frac{8}{2} = 4\ 	ext{rad/s}^2$$

Question 16

A $$1\ 	ext{kg}$$ object is lifted $$2\ 	ext{m}$$ vertically. How much work is done against gravity?

Accepted Answer

$$W = m g h = 1 	imes 9.8 	imes 2 = 19.6\ 	ext{J}$$

Question 17

A $$2\ 	ext{kg}$$ object is moving at $$3\ 	ext{m/s}$$ and is stopped by a constant force over $$6\ 	ext{m}. $$What is the magnitude of the force?

Accepted Answer

$$F = \frac{K}{d} = \frac{\frac{1}{2} 	imes 2 	imes 9}{6} = \frac{9}{6} = 1.5\ 	ext{N}$$

Question 18

A $$0.3\ 	ext{kg}$$ object is moving at $$2\ 	ext{m/s}$$ and collides with a wall, coming to rest in $$0.1\ 	ext{s}. $$What is the average force exerted by the wall?

Accepted Answer

$$F = \frac{\Delta p}{\Delta t} = \frac{0.3 	imes 2}{0.1} = 6\ 	ext{N}$$

Question 19

A $$0.5\ 	ext{kg}$$ object is dropped from $$10\ 	ext{m}$$ and lands with a velocity of $$14\ 	ext{m/s}. $$How much thermal energy $$E_{th}$$ was generated during the fall?

Accepted Answer

$$E_{th} = m g h - \frac{1}{2} m v^2$ = 0.5 	imes 9.8 	imes 10 - 0.5 	imes 14^2$ = 49 - 98 = -49\ 	ext{J} ($$energy lost to air resistance)

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