# Chapter Review

### Concept Items

#### 5.1 Vector Addition and Subtraction: Graphical Methods

- $$4.0
- $$5.8
- $$6.3
- $$8.0

- By joining the head of the first vector to the head of the last.
- By joining the head of the first vector with the tail of the last.
- By joining the tail of the first vector to the head of the last.
- By joining the tail of the first vector with the tail of the last.

- ${110}^{\circ}$
- ${160}^{\circ}$
- ${200}^{\circ}$
- ${290}^{\circ}$

#### 5.2 Vector Addition and Subtraction: Analytical Methods

- ${0}^{\circ}$
- ${45}^{\circ}$
- ${90}^{\circ}$
- ${180}^{\circ}$

- The magnitude of the resultant vector will be zero.
- The magnitude of resultant vector will be twice the magnitude of the original vector.
- The magnitude of resultant vector will be same as magnitude of the original vector.
- The magnitude of resultant vector will be half the magnitude of the original vector.

- ${A}_{x}=A\mathrm{cos}\theta $ ${A}_{y}=A\mathrm{sin}\theta $
- ${A}_{x}=A\mathrm{cos}\theta $ ${A}_{y}=A\mathrm{cos}\theta $
- ${A}_{x}=A\mathrm{sin}\theta $ ${A}_{y}=A\mathrm{cos}\theta $
- ${A}_{x}=A\mathrm{sin}\theta $ ${A}_{y}=A\mathrm{sin}\theta $

True or False—Every 2-D vector can be expressed as the product of its x and y-components.

- True
- False

#### 5.3 Projectile Motion

- Any object in projectile motion falls at the same rate as an object in freefall, regardless of its horizontal velocity.
- All objects in projectile motion fall at different rates, regardless of their initial horizontal velocities.
- Any object in projectile motion falls at the same rate as its initial vertical velocity, regardless of its initial horizontal velocity.
- All objects in projectile motion fall at different rates and the rate of fall of the object is independent of the initial velocity.

- $-9.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $-9.8\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$
- $9.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $9.8\phantom{\rule{thinmathspace}{0ex}}{\text{m/s}}^{2}$

#### 5.4 Inclined Planes

True or False—Kinetic friction is less than the limiting static friction because once an object is moving, there are fewer points of contact, and the friction is reduced. For this reason, more force is needed to start moving an object than to keep it in motion.

- True
- False

- ${f}_{\text{s}}\le N$
- ${f}_{s}\le {\mu}_{\text{s}}N$
- ${f}_{s}\ge N$
- ${f}_{s}\ge {\mu}_{\text{s}}N$

- ${f}_{\text{k}}={\mu}_{\text{s}}N$
- ${f}_{\text{k}}={\mu}_{\text{k}}N$
- ${f}_{\text{k}}\le {\mu}_{\text{s}}N$
- ${f}_{\text{k}}\le {\mu}_{\text{k}}N$

#### 5.5 Simple Harmonic Motion

- The negative sign indicates that displacement decreases with increasing force.
- The negative sign indicates that the direction of the applied force is opposite to that of displacement.
- The negative sign indicates that the direction of the restoring force is opposite to that of displacement.
- The negative sign indicates that the force constant must be negative.

With reference to simple harmonic motion, what is the equilibrium position?

- The position where velocity is the minimum
- The position where the displacement is maximum
- The position where the restoring force is the maximum
- The position where the object rests in the absence of force

- Restoring force is directly proportional to the displacement from the mean position and acts in the the opposite direction of the displacement.
- Restoring force is directly proportional to the displacement from the mean position and acts in the same direction as the displacement.
- Restoring force is directly proportional to the square of the displacement from the mean position and acts in the opposite direction of the displacement.
- Restoring force is directly proportional to the square of the displacement from the mean position and acts in the same direction as the displacement.

### Critical Thinking Items

#### 5.1 Vector Addition and Subtraction: Graphical Methods

True or False—A person is following a set of directions. He has to walk 2 km east and then 1 km north. He takes a wrong turn and walks in the opposite direction for the second leg of the trip. The magnitude of his total displacement will be the same as it would have been had he followed directions correctly.

- True
- False

#### 5.2 Vector Addition and Subtraction: Analytical Methods

- $1.0\phantom{\rule{thinmathspace}{0ex}}\text{units}$
- $2.0\phantom{\rule{thinmathspace}{0ex}}\text{units}$
- $2.3\phantom{\rule{thinmathspace}{0ex}}\text{units}$
- $4.0\phantom{\rule{thinmathspace}{0ex}}\text{units}$

- $\overrightarrow{\text{A}}$
- $\overrightarrow{\text{B}}$

#### 5.3 Projectile Motion

- Object 1 will hit the ground $3.2\phantom{\rule{thinmathspace}{0ex}}\text{s}$ after object 2.
- Object 1 will hit the ground $2.1\phantom{\rule{thinmathspace}{0ex}}\text{s}$ after object 2.
- Object 1 will hit the ground at the same time as object 2.
- Object 1 will hit the ground $1.1\phantom{\rule{thinmathspace}{0ex}}\text{s}$ after object 2.

An object is launched into the air. If the y-component of its acceleration is 9.8 m/s^{2}, which direction is defined as positive?

- Vertically upward in the coordinate system
- Vertically downward in the coordinate system
- Horizontally to the right side of the coordinate system
- Horizontally to the left side of the coordinate system

#### 5.4 Inclined Planes

- ${\mu}_{\text{k}}=0$
- ${\mu}_{\text{k}}=0.2$
- ${\mu}_{\text{k}}<0.2$
- ${\mu}_{\text{k}}>0.2$

- $10.9\phantom{\rule{thinmathspace}{0ex}}\text{kg}$
- $29.8\phantom{\rule{thinmathspace}{0ex}}\text{kg}$
- $106\phantom{\rule{thinmathspace}{0ex}}\text{kg}$
- $292\phantom{\rule{thinmathspace}{0ex}}\text{kg}$

#### 5.5 Simple Harmonic Motion

- Spring A will have more extension than spring B.
- Spring B will have more extension than spring A.
- Both springs will have equal extension.
- Both springs are equally stiff.

- The spring on the left will oscillate faster than spring on the right.
- The spring on the right will oscillate faster than the spring on the left.
- Both the springs will oscillate at the same rate.
- The rate of oscillation is independent of the force constant.

### Problems

#### 5.1 Vector Addition and Subtraction: Graphical Methods

- The resultant velocity of the boat will be $10.0\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$. The boat will go toward his right at an angle of ${26.6}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ to a line drawn across the river.
- The resultant velocity of the boat will be $10.0\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$. The boat will go toward his left at an angle of ${26.6}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ to a line drawn across the river.
- The resultant velocity of the boat will be $15.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$. The boat will go toward his right at an angle of ${18.4}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ to a line drawn across the river.
- The resultant velocity of the boat will be $15.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$. The boat will go toward his left at an angle of ${18.4}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ to a line drawn across the river.

- It should head in a direction ${22.6}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ east of south.
- It should head in a direction ${22.6}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ south of east.
- It should head in a direction ${45.0}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ east of south.
- It should head in a direction ${45.0}^{\circ}$ south of east.

#### 5.2 Vector Addition and Subtraction: Analytical Methods

- $\left|\overrightarrow{\text{R}}\right|=10.2\phantom{\rule{thinmathspace}{0ex}}\text{m}$, $\theta ={78.7}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ east of north
- $\left|\overrightarrow{\text{R}}\right|=10.2\phantom{\rule{thinmathspace}{0ex}}\text{m}$, $\theta ={78.7}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ north of east
- $\left|\overrightarrow{\text{R}}\right|=12.0\phantom{\rule{thinmathspace}{0ex}}\text{m}$, $\theta ={78.7}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ east of north
- $\left|\overrightarrow{\text{R}}\right|=12.00\phantom{\rule{thinmathspace}{0ex}}\text{m}$, $\theta ={78.7}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ north of east

- $10.84\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $65.1\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $66.04\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $80.00\phantom{\rule{thinmathspace}{0ex}}\text{m}$

#### 5.3 Projectile Motion

- $2.35\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $3.01\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $70.35\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $90.44\phantom{\rule{thinmathspace}{0ex}}\text{m}$

A person wants to fire a water balloon cannon such that it hits a target 100 m away. If the cannon can only be launched at 45° above the horizontal, what should be the initial speed at which it is launched?

- 31.3 m/s
- 37.2 m/s
- 980.0 m/s
- 1,385.9 m/s

#### 5.4 Inclined Planes

- ${\mu}_{\text{k}}=0$
- ${\mu}_{\text{k}}=0.18$
- ${\mu}_{\text{k}}=5.88$
- ${\mu}_{\text{k}}=\mathrm{\infty}$

A skier with a mass of 55 kg is skiing down a snowy slope that has an incline of 30°. Find the coefficient of kinetic friction for the skier if friction is known to be 25 N .

- $\mu k=0$
- $\mu k=0.05$
- $\mu k=0.09$
- $\mu k=\mathrm{\infty}$

#### 5.5 Simple Harmonic Motion

- $0.08\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $0.49\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $4.9\phantom{\rule{thinmathspace}{0ex}}\text{s}$
- $80\phantom{\rule{thinmathspace}{0ex}}\text{s}$

- $0.125\phantom{\rule{thinmathspace}{0ex}}\text{N/m}$
- $0.202\phantom{\rule{thinmathspace}{0ex}}\text{N/m}$
- $0.81\phantom{\rule{thinmathspace}{0ex}}\text{N/m}$
- $4.93\phantom{\rule{thinmathspace}{0ex}}\text{N/m}$

### Performance Task

fs-id1167066873855b#### 5.5 Simple Harmonic Motion

Construct a seconds pendulum (pendulum with time period 2 seconds).