### Concept Items

#### 4.1 Force

What is dynamics?

- Dynamics is the study of internal forces.
- Dynamics is the study of forces and their effect on motion.
- Dynamics describes the motion of points, bodies, and systems without consideration of the cause of motion.
- Dynamics describes the effect of forces on each other.

Two forces acting on an object are perpendicular to one another. How would you draw these in a free-body diagram?

- The two force arrows will be drawn at a right angle to one another.
- The two force arrows will be pointing in opposite directions.
- The two force arrows will be at a 45° angle to one another.
- The two force arrows will be at a 180° angle to one another.

A free-body diagram shows the forces acting on an object. How is that object represented in the diagram?

- A single point
- A square box
- A unit circle
- The object as it is

#### 4.2 Newton's First Law of Motion: Inertia

A ball rolls along the ground, moving from north to south. What direction is the frictional force that acts on the ball?

- North to south
- South to north
- West to east
- East to west

The tires you choose to drive over icy roads will create more friction with the road than your summer tires. Give another example where more friction is desirable.

- Children’s slide
- Air hockey table
- Ice-skating rink
- Jogging track

How do you express, mathematically, that no external force is acting on a body?

- F
_{net}= −1 - F
_{net}= 0 - F
_{net}= 1 - F
_{net}= ∞

#### 4.3 Newton's Second Law of Motion

- When one variable increases, the other variable decreases by a greater amount.
- When one variable increases, the other variable also increases.
- When one variable increases, the other variable decreases by the same factor.
- When one variable increases, the other variable also increases by the same factor.

True or False—Newton’s second law can be interpreted based on Newton’s first law.

- True
- False

#### 4.4 Newton's Third Law of Motion

- internal forces
- external forces
- both internal and external forces
- neither internal nor external forces

True or False—Newton’s third law applies to the external forces acting on a system of interest.

- True
- False

- Upward
- Downward
- Right
- Left

### Critical Thinking Items

#### 4.1 Force

Only two forces are acting on an object: force A to the left and force B to the right. If force B is greater than force A, in which direction will the object move?

- To the right
- To the left
- Upward
- The object does not move

In a free-body diagram, the arrows representing tension and weight have the same length but point away from one another. What does this indicate?

- They are equal in magnitude and act in the same direction.
- They are equal in magnitude and act in opposite directions.
- They are unequal in magnitude and act in the same direction.
- They are unequal in magnitude and act in opposite directions.

An object is at rest. Two forces, X and Y, are acting on it. Force X has a magnitude of *x* and acts in the downward direction. What is the magnitude and direction of Y?

- The magnitude is
*x*and points in the upward direction. - The magnitude is 2
*x*and points in the upward direction. - The magnitude is
*x*and points in the downward direction. - The magnitude is 2
*x*and points in the downward direction.

Three forces, A, B, and C, are acting on the same object with magnitudes *a, b*, and *c*, respectively. Force A acts to the right, force B acts to the left, and force C acts downward. What is a necessary condition for the object to move straight down?

- The magnitude of force A must be greater than the magnitude of force B, so a > b.
- The magnitude of force A must be equal to the magnitude of force B, so a = b.
- The magnitude of force A must be greater than the magnitude of force C, so A > C.
- The magnitude of force C must be greater than the magnitude of forces A or B, so A < C > B.

#### 4.2 Newton's First Law of Motion: Inertia

Two people push a cart on a horizontal surface by applying forces F_{1} and F_{2} in the same direction. Is the magnitude of the net force acting on the cart, F_{net}, equal to, greater than, or less than F_{1} + F_{2}? Why?

- F
_{net}< F_{1}+ F_{2}because the net force will not include the frictional force. - F
_{net}= F_{1}+ F_{2}because the net force will not include the frictional force - F
_{net}< F_{1}+ F_{2}because the net force will include the component of frictional force - F
_{net}= F_{1}+ F_{2}because the net force will include the frictional force

True or False: A book placed on a balance scale is balanced by a standard 1-kg iron weight placed on the opposite side of the balance. If these objects are taken to the moon and a similar exercise is performed, the balance is still level because gravity is uniform on the moon’s surface as it is on Earth’s surface.

- True
- False

#### 4.3 Newton's Second Law of Motion

From the equation for Newton’s second law, we see that *F*_{net} is directly proportional to **a** and that the constant of proportionality is ** m**. What does this mean in a practical sense?

- An increase in applied force will cause an increase in acceleration if the mass is constant.
- An increase in applied force will cause a decrease in acceleration if the mass is constant.
- An increase in applied force will cause an increase in acceleration, even if the mass varies.
- An increase in applied force will cause an increase in acceleration and mass.

#### 4.4 Newton's Third Law of Motion

True or False: A person accelerates while walking on the ground by exerting force. The ground in turn exerts force F_{2} on the person. F_{1} and F_{2} are equal in magnitude but act in opposite directions. The person is able to walk because the two forces act on the different systems and the net force acting on the person is nonzero.

- True
- False

A helicopter pushes air down, which, in turn, pushes the helicopter up. Which force affects the helicopter’s motion? Why?

- Air pushing upward affects the helicopter’s motion because it is an internal force that acts on the helicopter.
- Air pushing upward affects the helicopter’s motion because it is an external force that acts on the helicopter.
- The downward force applied by the blades of the helicopter affects its motion because it is an internal force that acts on the helicopter.
- The downward force applied by the blades of the helicopter affects its motion because it is an external force that acts on the helicopter.

### Problems

#### 4.3 Newton's Second Law of Motion

- $1\phantom{\rule{thinmathspace}{0ex}}\text{N}$
- $1.67\phantom{\rule{thinmathspace}{0ex}}\text{N}$
- $9.8\phantom{\rule{thinmathspace}{0ex}}\text{N}$
- $10\phantom{\rule{thinmathspace}{0ex}}\text{N}$

A bathroom scale shows your mass as 55 kg. What will it read on the moon?

- 9.4 kg
- 10.5 kg
- 55.0 kg
- 91.9 kg

#### 4.4 Newton's Third Law of Motion

A person pushes an object of mass 5.0 kg along the floor by applying a force. If the object experiences a friction force of 10 N and accelerates at 18 m/s^{2}, what is the magnitude of the force exerted by the person?

- −90 N
- −80 N
- 90 N
- 100 N

### Performance Task

#### 4.4 Newton's Third Law of Motion

- $0.244\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $0.265\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $4.00\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $4.10\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$