Q: A ball is thrown vertically upward with an initial velocity of $v_0 = 20\ \mathrm{m/s}$. Neglecting air resistance, what is the maximum height reached by the ball? (Use $g = 9.8\ \mathrm{m/s^2}$)

$h_{max} = \dfrac{v_0^2}{2g} = \dfrac{(20)^2}{2 \times 9.8} = 20.4\ \mathrm{m}$

Q: A projectile is launched at an angle $\theta = 45^\circ$ with an initial speed $v_0 = 10\ \mathrm{m/s}$. What is the time of flight? (Neglect air resistance, $g = 9.8\ \mathrm{m/s^2}$)

$t = \dfrac{2 v_0 \sin \theta}{g} = \dfrac{2 \times 10 \times \sin 45^\circ}{9.8} \approx 1.44\ \mathrm{s}$

Q: A $2\ \mathrm{kg}$ block slides down a frictionless incline of height $5\ \mathrm{m}$. What is its speed at the bottom?

$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} \approx 9.9\ \mathrm{m/s}$

Q: A $3\ \mathrm{kg}$ object moving at $2\ \mathrm{m/s}$ collides inelastically with a $2\ \mathrm{kg}$ object at rest. What is the final velocity of the combined mass?

$v_f = \dfrac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = \dfrac{3 \times 2 + 2 \times 0}{3 + 2} = 1.2\ \mathrm{m/s}$

Q: A $0.2\ \mathrm{kg}$ mass attached to a $0.5\ \mathrm{m}$ string swings in a horizontal circle at $2\ \mathrm{m/s}$. What is the tension in the string?

$T = \dfrac{m v^2}{r} = \dfrac{0.2 \times 4}{0.5} = 1.6\ \mathrm{N}$

Q: A $10\ \mathrm{kg}$ box is pulled across a horizontal floor with a force of $50\ \mathrm{N}$ at an angle of $30^\circ$ above the horizontal. If the coefficient of kinetic friction is $\mu_k = 0.2$, what is the acceleration of the box?

$a = \dfrac{F \cos \theta - \mu_k m g}{m} = \dfrac{50 \times 0.866 - 0.2 \times 10 \times 9.8}{10} \approx 0.13\ \mathrm{m/s^2}$

Q: A $2\ \mathrm{kg}$ object moves in a circle of radius $0.5\ \mathrm{m}$ at $3\ \mathrm{m/s}$. What is its angular momentum?

$L = m v r = 2 \times 3 \times 0.5 = 3\ \mathrm{kg\cdot m^2/s}$

Question 1

A ball is thrown vertically upward with an initial velocity of $v_0 = 20\ \mathrm{m/s}$. Neglecting air resistance, what is the maximum height reached by the ball? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$h_{max} = \dfrac{v_0^2}{2g} = \dfrac{(20)^2}{2 	imes 9.8} = 20.4\ \mathrm{m}$

Question 2

A car accelerates uniformly from rest to a speed of $30\ \mathrm{m/s}$ in $10\ \mathrm{s}$. What is the car's acceleration?

Accepted Answer

$a = \dfrac{v_f - v_i}{t} = \dfrac{30 - 0}{10} = 3\ \mathrm{m/s^2}$

Question 3

A projectile is launched at an angle $	heta = 45^\circ$ with an initial speed $v_0 = 10\ \mathrm{m/s}$. What is the time of flight? (Neglect air resistance, $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$t = \dfrac{2 v_0 \sin 	heta}{g} = \dfrac{2 	imes 10 	imes \sin 45^\circ}{9.8} \approx 1.44\ \mathrm{s}$

Question 4

A $2\ \mathrm{kg}$ block slides down a frictionless incline of height $5\ \mathrm{m}$. What is its speed at the bottom?

Accepted Answer

$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9\ \mathrm{m/s}$

Question 5

A $0.5\ \mathrm{kg}$ ball moving at $4\ \mathrm{m/s}$ collides elastically with a stationary $0.5\ \mathrm{kg}$ ball. What is the velocity of the first ball after the collision?

Accepted Answer

$v_1' = 0\ \mathrm{m/s}$

Question 6

A $3\ \mathrm{kg}$ object moving at $2\ \mathrm{m/s}$ collides inelastically with a $2\ \mathrm{kg}$ object at rest. What is the final velocity of the combined mass?

Accepted Answer

$v_f = \dfrac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = \dfrac{3 	imes 2 + 2 	imes 0}{3 + 2} = 1.2\ \mathrm{m/s}$

Question 7

A $0.2\ \mathrm{kg}$ mass attached to a $0.5\ \mathrm{m}$ string swings in a horizontal circle at $2\ \mathrm{m/s}$. What is the tension in the string?

Accepted Answer

$T = \dfrac{m v^2}{r} = \dfrac{0.2 	imes 4}{0.5} = 1.6\ \mathrm{N}$

Question 8

A $5\ \mathrm{kg}$ object is acted on by a $20\ \mathrm{N}$ force. What is its acceleration?

Accepted Answer

$a = \dfrac{F}{m} = \dfrac{20}{5} = 4\ \mathrm{m/s^2}$

Question 9

A $10\ \mathrm{kg}$ box is pulled across a horizontal floor with a force of $50\ \mathrm{N}$ at an angle of $30^\circ$ above the horizontal. If the coefficient of kinetic friction is $\mu_k = 0.2$, what is the acceleration of the box?

Accepted Answer

$a = \dfrac{F \cos 	heta - \mu_k m g}{m} = \dfrac{50 	imes 0.866 - 0.2 	imes 10 	imes 9.8}{10} \approx 0.13\ \mathrm{m/s^2}$

Question 10

A $0.1\ \mathrm{kg}$ mass oscillates on a spring with $k = 40\ \mathrm{N/m}$. What is its period?

Accepted Answer

$T = 2\pi \sqrt{\dfrac{m}{k}} = 2\pi \sqrt{\dfrac{0.1}{40}} \approx 0.314\ \mathrm{s}$

Question 11

A $2\ \mathrm{kg}$ object moves in a circle of radius $0.5\ \mathrm{m}$ at $3\ \mathrm{m/s}$. What is its angular momentum?

Accepted Answer

$L = m v r = 2 	imes 3 	imes 0.5 = 3\ \mathrm{kg\cdot m^2/s}$

Question 12

A $0.3\ \mathrm{kg}$ mass is attached to a $0.4\ \mathrm{m}$ long string and swung in a vertical circle. At the lowest point, its speed is $5\ \mathrm{m/s}$. What is the tension in the string at this point?

Accepted Answer

$T = m g + \dfrac{m v^2}{r} = 0.3 	imes 9.8 + \dfrac{0.3 	imes 25}{0.4} = 2.94 + 18.75 = 21.69\ \mathrm{N}$

Question 13

A $0.5\ \mathrm{kg}$ block is attached to a spring ($k = 20\ \mathrm{N/m}$) and oscillates with amplitude $0.1\ \mathrm{m}$. What is the maximum kinetic energy?

Accepted Answer

$K_{max} = \dfrac{1}{2} k A^2 = \dfrac{1}{2} 	imes 20 	imes (0.1)^2 = 0.1\ \mathrm{J}$

Question 14

A $1\ \mathrm{kg}$ object is dropped from a height of $10\ \mathrm{m}$. What is its velocity just before hitting the ground? (Neglect air resistance)

Accepted Answer

$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} \approx 14\ \mathrm{m/s}$

Question 15

A $0.2\ \mathrm{kg}$ mass oscillates with a frequency of $5\ \mathrm{Hz}$. What is the spring constant $k$?

Accepted Answer

$k = (2\pi f)^2 m = (2\pi 	imes 5)^2 	imes 0.2 = (31.42)^2 	imes 0.2 \approx 197.4\ \mathrm{N/m}$

Question 16

A $0.5\ \mathrm{kg}$ block slides $2\ \mathrm{m}$ down a ramp inclined at $30^\circ$ to the horizontal. What is the work done by gravity?

Accepted Answer

$W = m g d \sin 	heta = 0.5 	imes 9.8 	imes 2 	imes 0.5 = 4.9\ \mathrm{J}$

Question 17

A $1\ \mathrm{kg}$ mass is attached to a $2\ \mathrm{m}$ long string and swung in a horizontal circle at $4\ \mathrm{m/s}$. What is the centripetal acceleration?

Accepted Answer

$a_c = \dfrac{v^2}{r} = \dfrac{16}{2} = 8\ \mathrm{m/s^2}$

Question 18

A $0.4\ \mathrm{kg}$ mass is attached to a spring ($k = 10\ \mathrm{N/m}$) and oscillates with amplitude $0.2\ \mathrm{m}$. What is the total mechanical energy?

Accepted Answer

$E = \dfrac{1}{2} k A^2 = \dfrac{1}{2} 	imes 10 	imes (0.2)^2 = 0.2\ \mathrm{J}$

Physics I Syllabus and Course Structure: Mechanics, Energy, and Oscillations

Study Guide - Practice Questions

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