Q: Given a vector $$\vec{A}$$ with magnitude $$A at an $$angle $$\theta$$ above the horizontal, what are its $$x$$ and $$y$$ components?

$$A_x = A \cos\theta$$, $$A_y = A \sin\theta$$

Q: Which equation correctly expresses Newton's Second Law for motion in two dimensions?

$$F_{x,\text{net}} = m a_x$$ and $$F_{y,\text{net}} = m a_y$$

Question 1

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

Accepted Answer

An object at rest will remain at rest, and an object in motion will continue moving in a straight line at constant speed unless acted upon by a net external force.

Question 2

A 2.0 kg block is pulled by a constant force of 10 N on a frictionless surface. What is its acceleration?

Accepted Answer

$$a = \frac{10\,\mathrm{N}}{2.0\,\mathrm{kg}} = 5.0\,\mathrm{m/s^2$}$$

Question 3

A glider of mass $$m_1 = 1.0$$\,\mathrm{kg}$$ accelerates at 3.0$$\,\mathrm{$$m/s^2$$}$$ when pulled by a constant force. A second glider accelerates at 5.0$$\,\mathrm{$$m/s^2$$}$$ under the same force. What is the mass of the second glider?

Accepted Answer

$$m_2$$ = \frac{3.0\,\mathrm{$$m/s^2$$}}{5.0\,\mathrm{$$m/s^2$$}} 	imes 1.0\,\mathrm{kg} = 0.60\,\mathrm{kg}$$

Question 4

Which statement about force vectors is correct?

Accepted Answer

The force vector should be drawn as an arrow pointing in the direction the force acts, with length proportional to the magnitude of the force.

Question 5

A basketball is dropped while a strong wind blows horizontally to the right. Which direction does the ball accelerate?

Accepted Answer

Diagonally downward and to the right, due to the combined effect of gravity and wind.

Question 6

A Boeing 737 with mass $$51,000\,\mathrm{kg}$$ accelerates down a runway and reaches $$70\,\mathrm{m/s}$$ after traveling $$940\,\mathrm{m}. $$Assuming constant acceleration, what is the thrust produced by both engines together?

Accepted Answer

$$F = ma = (51,000\,\mathrm{kg})(2.61\,\mathrm{m/s^2$}) = 133,000\,\mathrm{N}$$

Question 7

Which of the following is NOT a common force identified in free-body diagrams?

Accepted Answer

Momentum

Question 8

If a box is being pulled to the right at constant velocity on a rough surface, which statement is true about the forces acting on it?

Accepted Answer

The net force on the box is zero.

Question 9

Given a vector $$\vec{A}$$ with magnitude $$A at an $$angle $$	heta$$ above the horizontal, what are its $$x$$ and $$y$$ components?

Accepted Answer

$$A_x = A \cos	heta$$, $$A_y = A \sin	heta$$

Question 10

A ball is hanging from the ceiling by a rope and is pulled back and released. Which forces act on the ball at the moment it is released?

Accepted Answer

Tension and weight

Question 11

Which equation correctly expresses Newton's Second Law for motion in two dimensions?

Accepted Answer

$$F_{x,	ext{net}} = m a_x$$ and $$F_{y,	ext{net}} = m a_y$$

Question 12

A car is parked on a hill. Which force acts perpendicular to the surface of the hill?

Accepted Answer

Normal force

Question 13

If the net force on an object is zero, what can be said about its motion?

Accepted Answer

It must be moving at constant velocity or at rest.

Question 14

A vector has components $$A_x = 3$$ and $$A_y = 4. $$What is its magnitude?

Accepted Answer

$$A = \sqrt{A_x^2$ + A_y^2$} = \sqrt{3^2$ + 4^2$} = 5$$

Question 15

Which of the following is a correct step in drawing a free-body diagram?

Accepted Answer

Represent the object as a dot at the origin of the coordinate system.

Question 16

A box is in free fall. Which forces act on it?

Accepted Answer

Only the weight force (gravity).

Question 17

A spring pushes a box to the right on a frictionless surface. If the spring exerts a force $$F$$ and the box has mass $$m$$, what is the acceleration of the box?

Accepted Answer

$$a = \frac{F}{m}$$

Question 18

Which of the following is a correct use of trigonometry to find the angle of a vector from its components?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{A_y}{A_x}ight)$$

Question 19

A person pulls a sled on ice with a constant force. If the ice becomes smoother, what happens to the distance the sled slides?

Accepted Answer

The sled slides farther because friction decreases.

Force and Motion: Newton's Laws and Vector Analysis

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