Q: A $$2\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is its speed at the bottom?

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

Q: A $$0.2\ \mathrm{kg}$$ mass attached to a spring oscillates with a period of $$0.5\ \mathrm{s}. $$What is the spring constant $$k$$?

$$k = \dfrac{4\pi^2$ m}{T^2$} = \dfrac{4 \times \pi^2$ \times 0.2}{0.25} \approx 31.6\ \mathrm{N/m}$$

Q: A $$5\ \mathrm{kg}$$ object is rotating at $$2\ \mathrm{rad/s}$$ about an axis $$0.5\ \mathrm{m}$$ from its center. What is its moment of inertia?

$$I = mr^2$ = 5 \times 0.5^2$ = 1.25\ \mathrm{kg\cdot m^2$}$$

Q: A $$0.5\ \mathrm{kg}$$ mass is attached to a string and swung in a horizontal circle of radius $$1\ \mathrm{m} at a $$speed of $$2\ \mathrm{m/s}. $$What is the tension in the string?

$$T = \dfrac{mv^2$}{r} = \dfrac{0.5 \times 4}{1} = 2\ \mathrm{N}$$

Question 1

A car accelerates uniformly from rest to a velocity of $$20\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the car's displacement during this time?

Accepted Answer

$$100\ \mathrm{m}$$

Question 2

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

Accepted Answer

The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass: $$F = ma$$

Question 3

A $$2\ \mathrm{kg}$$ block slides down a frictionless incline of height $$5\ \mathrm{m}. $$What is its speed at the bottom?

Accepted Answer

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

Question 4

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

$$0\ \mathrm{m/s}$$

Question 5

Which equation correctly relates angular velocity $$\omega to $$linear velocity $$v$$ for a point at radius $$r$$ from the axis of rotation?

Accepted Answer

$$v = r \omega$$

Question 6

A $$3\ \mathrm{kg}$$ object is moving at $$2\ \mathrm{m/s}. $$What is its momentum?

Accepted Answer

$$6\ \mathrm{kg\cdot m/s}$$

Question 7

A $$10\ \mathrm{kg}$$ child sits $$2\ \mathrm{m}$$ from the center of a seesaw, while a $$20\ \mathrm{kg}$$ child sits on the opposite side. How far from the center should the heavier child sit to balance the seesaw?

Accepted Answer

$$1\ \mathrm{m}$$

Question 8

Which of the following is a correct statement about equilibrium?

Accepted Answer

The net force and net torque on the object must both be zero.

Question 9

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

Accepted Answer

$$k = \dfrac{4\pi^2$ m}{T^2$} = \dfrac{4 	imes \pi^2$ 	imes 0.2}{0.25} \approx 31.6\ \mathrm{N/m}$$

Question 10

Which principle is used to solve problems involving collisions and explosions?

Accepted Answer

Conservation of linear momentum

Question 11

A $$5\ \mathrm{kg}$$ object is rotating at $$2\ \mathrm{rad/s}$$ about an axis $$0.5\ \mathrm{m}$$ from its center. What is its moment of inertia?

Accepted Answer

$$I = mr^2$ = 5 	imes 0.5^2$ = 1.25\ \mathrm{kg\cdot m^2$}$$

Question 12

Which of the following best describes the scientific method in physics?

Accepted Answer

A process involving observation, hypothesis, experimentation, and analysis.

Question 13

A $$1\ \mathrm{kg}$$ block is dropped from a height of $$10\ \mathrm{m}. $$What is its kinetic energy just before hitting the ground?

Accepted Answer

$$100\ \mathrm{J}$$

Question 14

Which equation represents the principle of conservation of energy for a closed system?

Accepted Answer

$$E_{initial} = E_{final}$$

Question 15

A $$0.5\ \mathrm{kg}$$ mass is attached to a string and swung in a horizontal circle of radius $$1\ \mathrm{m} at a $$speed of $$2\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = \dfrac{mv^2$}{r} = \dfrac{0.5 	imes 4}{1} = 2\ \mathrm{N}$$

Question 16

Which of the following is NOT a requirement for an object to be in static equilibrium?

Accepted Answer

The object must be moving at constant velocity.

Question 17

A $$2\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides inelastically with a $$1\ \mathrm{kg}$$ object at rest. What is their final velocity?

Accepted Answer

$$v = \dfrac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \dfrac{2 	imes 3 + 1 	imes 0}{2 + 1} = 2\ \mathrm{m/s}$$

Question 18

Which law explains why astronauts experience weightlessness while orbiting Earth?

Accepted Answer

Newton's Second Law (objects in free fall experience only gravity, so apparent weight is zero)

Question 19

A $$0.3\ \mathrm{kg}$$ mass oscillates on a spring with a frequency of $$2\ \mathrm{Hz}. $$What is the period of oscillation?

Accepted Answer

$$T = \dfrac{1}{f} = \dfrac{1}{2} = 0.5\ \mathrm{s}$$

Question 20

Which of the following is a correct application of the principle of heat and thermodynamics?

Accepted Answer

Energy transfer as heat occurs from higher to lower temperature.

Core Concepts and Problem-Solving in College Physics

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