Q: A ball is thrown horizontally from a cliff with a speed of 5 m/s. If the cliff is 20 m high, how long does it take for the ball to hit the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 20}{9.8}} \approx 2.02\ \mathrm{s}$$

Q: A 10 kg box is pulled across a horizontal surface with a force of 50 N. If the coefficient of kinetic friction is 0.2, what is the acceleration of the box?

$$a = \frac{F - f_k}{m} = \frac{50 - (0.2 \times 10 \times 9.8)}{10} = \frac{50 - 19.6}{10} = 3.04\ \mathrm{m/s^2$}$$

Q: A projectile is launched at an angle of $$30^\circ$$ with an initial speed of 40 m/s. What is the maximum height reached by the projectile? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g} = \frac{40^2$ \sin^2$ 30^\circ}{2 \times 9.8} = \frac{1600 \times 0.25}{19.6} = \frac{400}{19.6} \approx 20.4\ \mathrm{m}$$

Q: A block of mass 3 kg slides down a frictionless incline of height 5 m. What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = \sqrt{98} \approx 9.9\ \mathrm{m/s}$$

Question 1

A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the car's acceleration?

Accepted Answer

$$a = \frac{20}{10} = 2\ \mathrm{m/s^2$}$$

Question 2

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

Accepted Answer

An object in motion stays in motion unless acted upon by an unbalanced force.

Question 3

A ball is thrown horizontally from a cliff with a speed of 5 m/s. If the cliff is 20 m high, how long does it take for the ball to hit the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 20}{9.8}} \approx 2.02\ \mathrm{s}$$

Question 4

A 10 kg box is pulled across a horizontal surface with a force of 50 N. If the coefficient of kinetic friction is 0.2, what is the acceleration of the box?

Accepted Answer

$$a = \frac{F - f_k}{m} = \frac{50 - (0.2 	imes 10 	imes 9.8)}{10} = \frac{50 - 19.6}{10} = 3.04\ \mathrm{m/s^2$}$$

Question 5

Which of the following is a correct statement of the Work-Energy Theorem?

Accepted Answer

The net work done on an object is equal to its change in kinetic energy: $$W_{net} = \Delta K$$

Question 6

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

Accepted Answer

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

Question 7

A projectile is launched at an angle of $$30^\circ$$ with an initial speed of 40 m/s. What is the maximum height reached by the projectile? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g} = \frac{40^2$ \sin^2$ 30^\circ}{2 	imes 9.8} = \frac{1600 	imes 0.25}{19.6} = \frac{400}{19.6} \approx 20.4\ \mathrm{m}$$

Question 8

Which of the following is true about conservation of momentum in a collision?

Accepted Answer

The total momentum of the system before the collision equals the total momentum after the collision, provided no external forces act.

Question 9

A 0.5 kg ball moving at 10 m/s collides head-on with a stationary 0.5 kg ball. If the collision is perfectly elastic, what is the velocity of the first ball after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ + \frac{2m_2}{$$m_1$$ + $$m_2$$} $$v_2 = 0 + 0 = 0$$\ \mathrm{m/s}$$

Question 10

A block of mass 3 kg slides down a frictionless incline of height 5 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} = \sqrt{98} \approx 9.9\ \mathrm{m/s}$$

Question 11

Which of the following is the correct formula for Hooke's Law?

Accepted Answer

$$F = -kx$$

Question 12

A 4 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 4 	imes 9 = 18\ \mathrm{J}$$

Question 13

A pendulum has a length of 2 m. What is its period?

Accepted Answer

$$T = 2\pi \sqrt{\frac{l}{g}} = 2\pi \sqrt{\frac{2}{9.8}} \approx 2.84\ \mathrm{s}$$

Question 14

Which of the following statements about energy conservation is correct?

Accepted Answer

In a closed system, the total energy remains constant, though it may change forms.

Question 15

A 5 kg object is dropped from a height of 8 m. What is its velocity just before hitting the ground? (Ignore air resistance)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 8} = \sqrt{156.8} \approx 12.5\ \mathrm{m/s}$$

Question 16

Which of the following is the correct expression for the mechanical energy of a simple pendulum at its highest point?

Accepted Answer

$$E = mgh$$

Question 17

A 1 kg mass is attached to a string and swung in a horizontal circle of radius 2 m at a speed of 4 m/s. What is the tension in the string?

Accepted Answer

$$T = \frac{mv^2$}{r} = \frac{1 	imes 16}{2} = 8\ \mathrm{N}$$

Question 18

Which of the following is the correct formula for the impulse delivered to an object?

Accepted Answer

$$J = F \Delta t$$

PHYS 2333: College Physics I – Course Overview and Study Guide

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