Q: A car of mass $$1200\ \mathrm{kg}$$ accelerates from rest to $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the net force acting on the car?

$$F = m a = 1200 \times \frac{20}{10} = 2400\ \mathrm{N}$$

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 $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$What is the maximum height it reaches? (Ignore air resistance)

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 \times 9.8} \approx 5.1\ \mathrm{m}$$

Q: A $$5\ \mathrm{kg}$$ object is moving in a circle of radius $$2\ \mathrm{m} at a $$speed of $$3\ \mathrm{m/s}. $$What is the centripetal force acting on it?

$$F_c = \frac{m v^2$}{r} = \frac{5 \times 3^2$}{2} = 22.5\ \mathrm{N}$$

Question 1

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. $$F_{net} = 0 \implies v = 	ext{constant}$$

Question 2

A car of mass $$1200\ \mathrm{kg}$$ accelerates from rest to $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the net force acting on the car?

Accepted Answer

$$F = m a = 1200 	imes \frac{20}{10} = 2400\ \mathrm{N}$$

Question 3

Which of the following scenarios best illustrates the concept of rotational equilibrium?

Accepted Answer

A seesaw balanced with equal weights at equal distances from the pivot, so $$\sum 	au = 0$$

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

Which equation correctly relates work, force, and displacement when the force is constant and parallel to the displacement?

Accepted Answer

$$W = F d$$

Question 6

A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$What is the maximum height it reaches? (Ignore air resistance)

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 	imes 9.8} \approx 5.1\ \mathrm{m}$$

Question 7

Which of the following best describes the principle of conservation of momentum in a closed system?

Accepted Answer

The total momentum before an interaction equals the total momentum after, $$\sum p_{initial} = \sum p_{final}$$

Question 8

A $$3\ \mathrm{kg}$$ object moving at $$4\ \mathrm{m/s}$$ collides elastically with a stationary $$2\ \mathrm{kg}$$ object. What is the velocity of the $$3\ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{3 - 2}{3 + 2} 	imes 4 = 0.8\ \mathrm{m/s}$$

Question 9

Which of the following is the correct formula for the period of a simple pendulum of length $$L$$?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 10

A $$5\ \mathrm{kg}$$ object is moving in a circle of radius $$2\ \mathrm{m} at a $$speed of $$3\ \mathrm{m/s}. $$What is the centripetal force acting on it?

Accepted Answer

$$F_c = \frac{m v^2$}{r} = \frac{5 	imes 3^2$}{2} = 22.5\ \mathrm{N}$$

Question 11

Which of the following statements about gravitational force is correct?

Accepted Answer

Gravitational force is always attractive and is given by $$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 12

A $$10\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$50\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$F_x = F \cos 	heta = 50 \cos 30^\circ = 50 	imes 0.866 = 43.3\ \mathrm{N}$$

Question 13

Which of the following is the correct expression for kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} m v^2$

Question 14

A $$0.2\ \mathrm{kg}$$ mass attached to a spring oscillates with an amplitude of $$0.1\ \mathrm{m}$$ and a period of $$0.5\ \mathrm{s}. $$What is the maximum speed of the mass?

Accepted Answer

$$v_{max} = \frac{2\pi A}{T} = \frac{2\pi 	imes 0.1}{0.5} \approx 1.26\ \mathrm{m/s}$$

Question 15

Which of the following best describes the difference between static and kinetic friction?

Accepted Answer

Static friction prevents motion up to a maximum value, while kinetic friction acts during motion and is usually less than maximum static friction.

Question 16

A $$1\ \mathrm{kg}$$ object is dropped from a height of $$20\ \mathrm{m}. $$What is its velocity just before hitting the ground? (Ignore air resistance)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} \approx 19.8\ \mathrm{m/s}$$

Question 17

Which of the following is the correct formula for angular momentum of a rotating object?

Accepted Answer

$$L = I \omega$$

Question 18

A $$0.5\ \mathrm{kg}$$ mass moves in a circle of radius $$0.2\ \mathrm{m} at an $$angular velocity of $$10\ \mathrm{rad/s}. $$What is its angular momentum?

Accepted Answer

$$L = m r^2$ \omega = 0.5 	imes 0.2^2$ 	imes 10 = 0.2\ \mathrm{kg\cdot m^2$/s}$$

AP Physics C Mechanics Syllabus and Study Guide

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