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 $$0.2\ \mathrm{kg}$$ 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

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