Q: A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the car's acceleration?

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

Q: A projectile is launched horizontally from the top of a 45 m high cliff. How long does it take to reach the ground? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{9.8}} \approx 3.03\ \text{s}$$

Q: A 5 kg object is acted upon by a net force of 15 N. What is its acceleration?

$$a = \frac{F}{m} = \frac{15\ \text{N}}{5\ \text{kg}} = 3\ \text{m/s}^2$$

Q: A block slides down a frictionless incline of height 10 m. What is its speed at the bottom? (Assume $$g = 9.8\ \text{m/s}^2)$$

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

Q: A 10 kg box is pulled across a horizontal surface with a force of 40 N. The coefficient of kinetic friction is 0.2. What is the acceleration of the box?

$$a = \frac{F - f_k}{m} = \frac{40 - (0.2 \times 10 \times 9.8)}{10} = \frac{40 - 19.6}{10} = 2.04\ \text{m/s}^2$$

Q: A spring with spring constant $$k = 200\ \text{N/m} is $$compressed by 0.1 m. What is the potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Q: A 0.5 kg ball is dropped from a height of 2 m. What is its velocity just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2} \approx 6.26\ \text{m/s}$$

Question 1

A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the car's acceleration?

Accepted Answer

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

Question 2

Which of the following best describes Newton's First Law of Motion?

Accepted Answer

An object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force.

Question 3

A projectile is launched horizontally from the top of a 45 m high cliff. How long does it take to reach the ground? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03\ 	ext{s}$$

Question 4

A 5 kg object is acted upon by a net force of 15 N. What is its acceleration?

Accepted Answer

$$a = \frac{F}{m} = \frac{15\ 	ext{N}}{5\ 	ext{kg}} = 3\ 	ext{m/s}^2$$

Question 5

A block slides down a frictionless incline of height 10 m. What is its speed at the bottom? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

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

Question 6

A 2 kg object moving at 3 m/s collides elastically with a stationary 1 kg object. What is the velocity of the 2 kg object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{2 - 1}{2 + 1} 	imes 3 = 1\ 	ext{m/s}$$

Question 7

A satellite orbits Earth at a distance where the gravitational force equals the centripetal force required for circular motion. Which equation correctly relates the satellite's speed $$v to $$Earth's mass $$M$$ and orbital radius $$r$$?

Accepted Answer

$$v = \sqrt{\frac{GM}{r}}$$

Question 8

A 10 kg box is pulled across a horizontal surface with a force of 40 N. The coefficient of kinetic friction is 0.2. What is the acceleration of the box?

Accepted Answer

$$a = \frac{F - f_k}{m} = \frac{40 - (0.2 	imes 10 	imes 9.8)}{10} = \frac{40 - 19.6}{10} = 2.04\ 	ext{m/s}^2$$

Question 9

A spring with spring constant $$k = 200\ 	ext{N/m} is $$compressed by 0.1 m. What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 10

A 0.5 kg ball is dropped from a height of 2 m. What is its velocity just before hitting the ground? (Ignore air resistance, $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2} \approx 6.26\ 	ext{m/s}$$

Question 11

A 3 kg object moving at 4 m/s collides inelastically with a 2 kg object at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{3 	imes 4 + 2 	imes 0}{3 + 2} = \frac{12}{5} = 2.4\ 	ext{m/s}$$

Question 12

A disk of mass 2 kg and radius 0.5 m rotates at 10 rad/s. What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} 	imes \frac{1}{2} m r^2$ 	imes \$$omega^2$$ = \frac{1}{2} 	imes \frac{1}{2} 	imes 2 	imes (0.5)^2$ 	imes (10)^2$ = 12.5\ 	ext{J}$$

Question 13

A uniform beam of length 4 m and mass 20 kg is supported at its ends. A 60 kg person stands 1 m from the left end. What is the force on the right support?

Accepted Answer

$$F_{	ext{right}} = \frac{(20 	imes 9.8 	imes 2) + (60 	imes 9.8 	imes 1)}{4} = \frac{392 + 588}{4} = 245\ 	ext{N}$$

Question 14

A pendulum of length 1 m swings with small amplitude. What is its period? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$T = 2\pi \sqrt{\frac{l}{g}} = 2\pi \sqrt{\frac{1}{9.8}} \approx 2.01\ 	ext{s}$$

Question 15

A 0.3 kg mass attached to a spring oscillates with amplitude 0.2 m and spring constant 50 N/m. What is its maximum speed?

Accepted Answer

$$v_{	ext{max}} = A \omega = 0.2 	imes \sqrt{\frac{50}{0.3}} \approx 0.2 	imes 12.91 = 2.58\ 	ext{m/s}$$

Question 16

A 1 kg object moves in a circle of radius 2 m at a speed of 4 m/s. What is the net force acting on it?

Accepted Answer

$$F = \frac{mv^2$}{r} = \frac{1 	imes 4^2$}{2} = \frac{16}{2} = 8\ 	ext{N}$$

Question 17

A fluid flows through a pipe with cross-sectional area $$A_1 = 0.01$$\ 	ext{m}^2$$ at speed v_1$ = 2\ 	ext{m/s}. If $$the pipe narrows to $$A_2 = 0.005$$\ 	ext{m}^2$$, what is the speed v_2$ in the narrow section?

Accepted Answer

$$v_2$$ = \frac{$$A_1$$ $$v_1$$}{$$A_2$$} = \frac{0.01 	imes 2}{0.005} = 4\ 	ext{m/s}$$

Question 18

A 0.5 kg object is attached to a string and swung in a horizontal circle of radius 0.4 m. If it completes one revolution every 2 seconds, what is the tension in the string?

Accepted Answer

$$T = \frac{m v^2$}{r}$$, $$v = \frac{2\pi r}{T} = \frac{2\pi 	imes 0.4}{2} = 1.257\ 	ext{m/s}$$, $$T = \frac{0.5 	imes (1.257)^2$}{0.4} \approx 1.98\ 	ext{N}$$

PHY 121: Physics I – Mechanics (Course Syllabus and Structure)

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