Q: Which of the following best describes the condition for static equilibrium?

$$\sum F = 0$$ and $$\sum \tau = 0$$

Question 1

A car accelerates uniformly from rest to a velocity of $$20\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$2\ \mathrm{m/s^2$}$$

Question 2

A $$2\ \mathrm{kg}$$ block slides down a frictionless ramp inclined at $$30^\circ to $$the horizontal. What is the acceleration of the block parallel to the ramp?

Accepted Answer

$$a = g \sin 30^\circ = 4.9\ \mathrm{m/s^2$}$$

Question 3

A runner moves at $$5\ \mathrm{m/s}$$ east relative to the ground. A car moves at $$15\ \mathrm{m/s}$$ east relative to the ground. What is the velocity of the car relative to the runner?

Accepted Answer

$$10\ \mathrm{m/s}$$\ east

Question 4

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

Accepted Answer

An object at rest remains at rest, and an object in motion continues in a straight line at constant speed unless acted upon by a net force.

Question 5

A $$5\ \mathrm{kg}$$ object is acted on by a net force of $$20\ \mathrm{N}. $$What is its acceleration?

Accepted Answer

$$4\ \mathrm{m/s^2$}$$

Question 6

Two ice skaters, A and B, push off against each other. Skater A has twice the mass of skater B. If the force exerted by A on B is $$F$$, what is the force exerted by B on A?

Accepted Answer

$$F$$, but in the opposite direction

Question 7

A $$70\ \mathrm{kg}$$ person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$840\ \mathrm{N}$$

Question 8

A ball is thrown straight up. At the highest point, which of the following is true?

Accepted Answer

The velocity is zero, but the acceleration is $$-g$$

Question 9

A $$0.5\ \mathrm{kg}$$ ball falls at terminal speed. If the drag force is $$5\ \mathrm{N}$$ upward, what is the weight of the ball?

Accepted Answer

$$5\ \mathrm{N}$$

Question 10

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

Accepted Answer

$$32\ \mathrm{N}$$

Question 11

A satellite orbits Earth in a circular orbit of radius $$r. $$Which equation gives its orbital speed?

Accepted Answer

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

Question 12

A $$3\ \mathrm{kg}$$ object is attached to a spring with spring constant $$k = 150\ \mathrm{N/m}. If $$the spring is stretched $$0.2\ \mathrm{m}$$ from equilibrium, what is the force exerted by the spring?

Accepted Answer

$$-30\ \mathrm{N}$$

Question 13

A force of $$10\ \mathrm{N}$$ acts at an angle of $$60^\circ to $$the direction of displacement of $$2\ \mathrm{m}. $$How much work is done?

Accepted Answer

$$10\ \mathrm{J}$$

Question 14

A uniform beam of length $$4\ \mathrm{m}$$ and mass $$20\ \mathrm{kg} is $$supported at its center. A $$40\ \mathrm{kg}$$ mass is hung $$1\ \mathrm{m}$$ from one end. Where should a $$20\ \mathrm{kg}$$ mass be hung from the other end to balance the beam?

Accepted Answer

$$0.5\ \mathrm{m}$$ from the other end

Question 15

Which of the following is the correct expression for the moment of inertia $$I of a $$system of particles?

Accepted Answer

$$I = \sum m_i r_i^2$

Question 16

A disk rotates with angular velocity $$\omega = 10\ \mathrm{rad/s}. $$What is the linear speed of a point $$0.2\ \mathrm{m}$$ from the center?

Accepted Answer

$$2\ \mathrm{m/s}$$

Question 17

A $$0.1\ \mathrm{kg}$$ ball moving at $$10\ \mathrm{m/s}$$ strikes a wall and rebounds at $$-8\ \mathrm{m/s}. $$What is the impulse delivered to the ball?

Accepted Answer

$$-1.8\ \mathrm{kg\cdot m/s}$$

Question 18

A $$2\ \mathrm{kg}$$ mass is moving at $$3\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$9\ \mathrm{J}$$

Question 19

Which of the following best describes the condition for static equilibrium?

Accepted Answer

$$\sum F = 0$$ and $$\sum 	au = 0$$

Fundamental Concepts in Mechanics: Motion, Forces, Circular Motion, and Energy

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