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

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

Q: A car of mass $$m = 1200\ \mathrm{kg}$$ accelerates from rest to $$v = 25\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the average net force exerted on the car?

$$F_{net} = m \dfrac{\Delta v}{\Delta t} = 1200 \times \dfrac{25}{10} = 3000\ \mathrm{N}$$

Q: A block slides down a frictionless incline of height $$h = 5\ \mathrm{m}. $$What is its speed at the bottom? (Assume it starts from rest and $$g = 9.8\ \mathrm{m/s^2$})$$

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

Q: A $$2\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides elastically with a stationary $$1\ \mathrm{kg}$$ object. What is the velocity of the $$1\ \mathrm{kg}$$ object after the collision?

$$v = \dfrac{2m_2}{m_1$ + m_2$} v_1$ = \dfrac{2 \times 1}{2 + 1} \times 3 = 2\ \mathrm{m/s}$$

Q: A $$0.5\ \mathrm{kg}$$ ball is attached to a $$1.5\ \mathrm{m}$$ string and swung in a horizontal circle at a constant speed of $$4\ \mathrm{m/s}. $$What is the tension in the string?

$$T = m \dfrac{v^2$}{r} = 0.5 \times \dfrac{16}{1.5} = 5.33\ \mathrm{N}$$

Q: A $$5\ \mathrm{kg}$$ object is dropped from a height of $$10\ \mathrm{m}. $$What is its kinetic energy just before hitting the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$KE = mgh = 5 \times 9.8 \times 10 = 490\ \mathrm{J}$$

Q: A $$0.2\ \mathrm{kg}$$ puck slides on ice with a velocity of $$5\ \mathrm{m/s}$$ and collides inelastically with a stationary $$0.3\ \mathrm{kg}$$ puck. What is their final velocity after the collision?

$$v_f = \dfrac{m_1$ v_1$}{m_1$ + m_2$} = \dfrac{0.2 \times 5}{0.2 + 0.3} = 2\ \mathrm{m/s}$$

Question 1

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

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

Accepted Answer

An object at rest remains at rest and an object in motion remains in motion at constant velocity unless acted upon by a net external force.

Question 3

A car of mass $$m = 1200\ \mathrm{kg}$$ accelerates from rest to $$v = 25\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the average net force exerted on the car?

Accepted Answer

$$F_{net} = m \dfrac{\Delta v}{\Delta t} = 1200 	imes \dfrac{25}{10} = 3000\ \mathrm{N}$$

Question 4

A block slides down a frictionless incline of height $$h = 5\ \mathrm{m}. $$What is its speed at the bottom? (Assume it starts from rest and $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 5

Which of the following is a correct statement about the conservation of energy in a closed system?

Accepted Answer

The total energy of a closed system remains constant over time.

Question 6

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

Accepted Answer

$$v = \dfrac{2m_2}{m_1$ + m_2$} v_1$ = \dfrac{2 	imes 1}{2 + 1} 	imes 3 = 2\ \mathrm{m/s}$$

Question 7

A $$0.5\ \mathrm{kg}$$ ball is attached to a $$1.5\ \mathrm{m}$$ string and swung in a horizontal circle at a constant speed of $$4\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = m \dfrac{v^2$}{r} = 0.5 	imes \dfrac{16}{1.5} = 5.33\ \mathrm{N}$$

Question 8

A $$5\ \mathrm{kg}$$ object is dropped from a height of $$10\ \mathrm{m}. $$What is its kinetic energy just before hitting the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$KE = mgh = 5 	imes 9.8 	imes 10 = 490\ \mathrm{J}$$

Question 9

Which of the following scenarios best illustrates Newton's Third Law of Motion?

Accepted Answer

A swimmer pushes water backward, and the water pushes the swimmer forward.

Question 10

A $$0.2\ \mathrm{kg}$$ puck slides on ice with a velocity of $$5\ \mathrm{m/s}$$ and collides inelastically with a stationary $$0.3\ \mathrm{kg}$$ puck. What is their final velocity after the collision?

Accepted Answer

$$v_f = \dfrac{m_1$ v_1$}{m_1$ + m_2$} = \dfrac{0.2 	imes 5}{0.2 + 0.3} = 2\ \mathrm{m/s}$$

Question 11

A $$10\ \mathrm{kg}$$ box is pulled across a horizontal floor with a constant velocity by a force of $$40\ \mathrm{N}. $$What is the coefficient of kinetic friction between the box and the floor? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\mu_k = \dfrac{F}{mg} = \dfrac{40}{10 	imes 9.8} = 0.41$$

Question 12

Which of the following is the correct expression for the work done by a constant force $$F$$ acting over a displacement $$d at an $$angle $$	heta to $$the direction of the force?

Accepted Answer

$$W = F d \cos 	heta$$

Question 13

A $$0.5\ \mathrm{kg}$$ mass attached to a spring oscillates with an amplitude of $$0.2\ \mathrm{m}$$ and a period of $$1.5\ \mathrm{s}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \dfrac{4 \pi^2$ m}{T^2$} = \dfrac{4 	imes (3.14)^2$ 	imes 0.5}{(1.5)^2$} \approx 8.77\ \mathrm{N/m}$$

Question 14

A $$1\ \mathrm{kg}$$ ball is dropped from a height of $$2\ \mathrm{m}$$ and rebounds to a height of $$1.5\ \mathrm{m}. $$What is the coefficient of restitution?

Accepted Answer

$$e = \sqrt{\dfrac{h_{rebound}}{h_{drop}}} = \sqrt{\dfrac{1.5}{2}} = 0.87$$

Question 15

A $$3\ \mathrm{kg}$$ object moves in a circle of radius $$2\ \mathrm{m} at a $$speed of $$6\ \mathrm{m/s}. $$What is the centripetal acceleration?

Accepted Answer

$$a_c = \dfrac{v^2$}{r} = \dfrac{36}{2} = 18\ \mathrm{m/s^2$}$$

Question 16

A $$0.8\ \mathrm{kg}$$ object is moving at $$10\ \mathrm{m/s}$$ and comes to rest in $$4\ \mathrm{s}$$ due to a constant friction force. What is the magnitude of the friction force?

Accepted Answer

$$F = m \dfrac{\Delta v}{\Delta t} = 0.8 	imes \dfrac{10}{4} = 2\ \mathrm{N}$$

Question 17

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 18

A $$2\ \mathrm{kg}$$ mass is attached to a rope and swung in a vertical circle of radius $$1\ \mathrm{m}. At $$the lowest point, what is the tension in the rope if the speed is $$4\ \mathrm{m/s}$$? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$T = mg + m \dfrac{v^2$}{r} = 2 	imes 9.8 + 2 	imes \dfrac{16}{1} = 19.6 + 32 = 51.6\ \mathrm{N}$$

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