# Test Prep

### Multiple Choice

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

True or False—We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other.

- True
- False

True or False—The direction of the resultant vector depends on both the magnitude and direction of added vectors.

- True
- False

- $130\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$ north
- $130\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$ south
- $270\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$ north
- $270\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$ south

- $200\phantom{\rule{thinmathspace}{0ex}}\text{m}$ east
- $200\phantom{\rule{thinmathspace}{0ex}}\text{m}$ south
- $260\phantom{\rule{thinmathspace}{0ex}}\text{m}$ east
- $260\phantom{\rule{thinmathspace}{0ex}}\text{m}$ south

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

*x*-component of a vector with angle $\theta $ be greater than its y-component?

- ${0}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}<\theta <{45}^{\circ}$
- $\theta ={45}^{\circ}$
- ${45}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}<\theta <{60}^{\circ}$
- ${60}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}<\theta <{90}^{\circ}$

- ${R}_{x}+{R}_{y}=0$
- ${A}_{x}+{A}_{y}=\overrightarrow{\text{A}}$
- ${A}_{x}+{B}_{y}={B}_{x}+{A}_{y}$
- ${A}_{x}+{B}_{x}={R}_{x}$

What is the dimensionality of vectors used in the study of atmospheric sciences?

- One-dimensional
- Two-dimensional
- Three-dimensional

#### 5.3 Projectile Motion

After a projectile is launched in the air, in which direction does it experience constant, non-zero acceleration, ignoring air resistance?

- The x direction
- The y direction
- Both the x and y directions
- Neither direction

- ${v}_{y}=0$
- ${v}_{y}=\text{maximum}$
- ${v}_{x}=\text{maximum}$

A ball is thrown in the air at an angle of 40°. If the maximum height it reaches is 10 m, what must be its initial speed?

- 17.46 m/s
- 21.78 m/s
- 304.92 m/s
- 474.37 m/s

- $84.90\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $96.59\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $169.80\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $193.20\phantom{\rule{thinmathspace}{0ex}}\text{m}$

#### 5.4 Inclined Planes

For objects of identical masses but made of different materials, which of the following experiences the most static friction?

- Shoes on ice
- Metal on wood
- Teflon on steel

If an object sits on an inclined plane and no other object makes contact with the object, what is typically equal in magnitude to the component of the weight perpendicular to the plane?

- The normal force
- The total weight
- The parallel force of weight

A 5 kg box is at rest on the floor. The coefficient of static friction between the box and the floor is 0.4. A horizontal force of 50 N is applied to the box. Will it move?

- No, because the applied force is less than the maximum limiting static friction.
- No, because the applied force is more than the maximum limiting static friction.
- Yes, because the applied force is less than the maximum limiting static friction.
- Yes, because the applied force is more than the maximum limiting static friction.

A skier with a mass of 67 kg is skiing down a snowy slope with an incline of 37°. Find the friction if the coefficient of kinetic friction is 0.07.

- 27.66 N
- 34.70 N
- 36.71 N
- 45.96 N

#### 5.5 Simple Harmonic Motion

A change in which of the following is an example of deformation?

- Velocity
- Length
- Mass
- Weight

The units of amplitude are the same as those for which of the following measurements?

- Speed
- Displacement
- Acceleration
- Force

- ${15}^{\circ}$
- ${45}^{\circ}$
- ${75}^{\circ}$
- ${90}^{\circ}$

- Oscillation will not happen in the absence of friction.
- Oscillation will continue forever in the absence of friction.
- Oscillation will have changing amplitude in the absence of friction.
- Oscillation will cease after a certain amount of time in the absence of friction.

- $0.03\phantom{\rule{thinmathspace}{0ex}}\text{kg}$
- $1.60\phantom{\rule{thinmathspace}{0ex}}\text{kg}$
- $30.7\phantom{\rule{thinmathspace}{0ex}}\text{kg}$
- $63.0\phantom{\rule{thinmathspace}{0ex}}\text{kg}$

### Short Answer

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

- $$206 cm, $\theta ={119.0}^{\circ}$
- $$206 cm, $\theta ={125.0}^{\circ}$
- $$108 cm, $\theta ={119.0}^{\circ}$
- $$108 cm, $\theta ={125.0}^{\circ}$

- $$108 cm, $\theta ={119.1}^{\circ}$
- $$108 cm, $\theta ={201.8}^{\circ}$
- $$206 cm, $\theta ={119.1}^{\circ}$
- $$206 cm, $\theta ={201.8}^{\circ}$

Consider six vectors of 2 cm each, joined from head to tail making a hexagon. What would be the magnitude of the addition of these vectors?

- Zero
- Six
- Eight
- Twelve

Two people pull on ropes tied to a trolley, each applying 44 N of force. The angle the ropes form with each other is 39.5°. What is the magnitude of the net force exerted on the trolley?

- 0.0 N
- 79.6 N
- 82.8 N
- 88.0 N

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

True or False—A vector can form the shape of a right angle triangle with its x and y components.

- True
- False

True or False—All vectors have positive x and y components.

- True
- False

- ${R}_{x}=\frac{{A}_{x}}{{B}_{x}}$
- ${R}_{x}=\frac{{B}_{x}}{{A}_{x}}$
- ${R}_{x}={A}_{x}+{B}_{x}$
- ${R}_{x}={A}_{x}-{B}_{x}$

- ${R}_{y}=\frac{{A}_{y}}{{B}_{y}}$
- ${R}_{y}=\frac{{B}_{y}}{{A}_{y}}$
- ${R}_{y}={A}_{y}+{B}_{y}$
- ${R}_{y}={A}_{y}-{B}_{y}$

When a three dimensional vector is used in the study of atmospheric sciences, what is z?

- Altitude
- Heat
- Temperature
- Wind speed

Which method is not an application of vector calculus?

- To find the rate of change in atmospheric temperature
- To study changes in wind speed and direction
- To predict changes in atmospheric pressure
- To measure changes in average rainfall

#### 5.3 Projectile Motion

- $\overrightarrow{v}=\overrightarrow{a}t$
- $\overrightarrow{v}=\overrightarrow{{v}_{0}}+\overrightarrow{a}t$
- $\overrightarrow{v}+\overrightarrow{{v}_{0}}=\overrightarrow{a}t$
- $\overrightarrow{{v}_{0}}+\overrightarrow{v}+\overrightarrow{a}t$

In the equation for the maximum height of a projectile, what does ${v}_{0y}$ stand for?

$$h=\frac{{v}_{0}{{}_{y}}^{2}}{2g}$$- Initial velocity in the x direction
- Initial velocity in the y direction
- Final velocity in the x direction
- Final velocity in the y direction

True or False—Range is defined as the maximum vertical distance travelled by a projectile.

- True
- False

- ${0}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${30}^{\circ}$
- ${0}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${45}^{\circ}$
- ${90}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${0}^{\circ}$
- ${90}^{\circ}\phantom{\rule{negativethinmathspace}{0ex}}$ or ${45}^{\circ}$

#### 5.4 Inclined Planes

- $\text{N}$
- $\text{m/s}$
- ${\text{m/s}}^{2}$
- unitless

- It increases with the increase in the relative motion.
- It decreases with the increase in the relative motion.
- It remains constant and is independent of the relative motion.

- When the magnitude of the component of the weight along the slope is equal to the magnitude of the frictional force.
- When the magnitude of the component of the weight along the slope is greater than the magnitude of the frictional force.
- When the magnitude of the component of the weight perpendicular to the slope is less than the magnitude of the frictional force.
- When the magnitude of the component of the weight perpendicular to the slope is equal to the magnitude of the frictional force.

- ${0}^{\circ}$
- ${30}^{\circ}$
- ${60}^{\circ}$
- ${90}^{\circ}$

#### 5.5 Simple Harmonic Motion

What is the term used for changes in shape due to the application of force?

- Amplitude
- Deformation
- Displacement
- Restoring force

What is the restoring force?

- The normal force on the surface of an object
- The weight of a mass attached to an object
- Force which is applied to deform an object from its original shape
- Force which brings an object back to its equilibrium position

For a given oscillator, what are the factors that affect its period and frequency?

- Mass only
- Force constant only
- Applied force and mass
- Mass and force constant

For an object in simple harmonic motion, when does the maximum speed occur?

- At the extreme positions
- At the equilibrium position
- At the moment when the applied force is removed
- Midway between the extreme and equilibrium positions

What is the equilibrium position of a pendulum?

- When the tension in the string is zero
- When the pendulum is hanging straight down
- When the tension in the string is maximum
- When the weight of the mass attached is minimum

If a pendulum is displaced by an angle *θ*, what is the net restoring force it experiences?

*mg*sin*θ**mg*cos*θ*- –
*mg*sin*θ* - –
*mg*cos*θ*

### Extended Response

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

True or false—For vectors the order of addition is important.

- True
- False

Consider five vectors *a , b , c , d,* and *e.* Is it true or false that their addition always results in a vector with a greater magnitude than if only two of the vectors were added?

- True
- False

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

- $\theta ={0}^{\circ}$
- $\theta ={45}^{\circ}$
- $\theta ={60}^{\circ}$
- $\theta ={90}^{\circ}$

True or False—If only the angles of two vectors are known, we can find the angle of their resultant addition vector.

- True
- False

True or False—We can find the magnitude and direction of the resultant vector if we know the angles of two vectors and the magnitude of one.

- True
- False

#### 5.3 Projectile Motion

- The x-component of the acceleration of a projectile is $0$ because acceleration of a projectile is due to gravity, which acts in the y direction.
- The x component of the acceleration of a projectile is $g$ because acceleration of a projectile is due to gravity, which acts in the x direction.
- The x-component of the acceleration of a projectile is $0$ because acceleration of a projectile is due to gravity, which acts in the x direction.
- The x-component of the acceleration of a projectile is $g$ because acceleration of a projectile is due to gravity, which acts in the y direction.

- ${0}^{\circ}$
- ${45}^{\circ}$
- ${60}^{\circ}$
- ${90}^{\circ}$

#### 5.4 Inclined Planes

True or False—Friction varies from surface to surface because different substances have different degrees of roughness or smoothness.

- True
- False

- Both the perpendicular and the parallel component will decrease.
- The perpendicular component will decrease and the parallel component will increase.
- The perpendicular component will increase and the parallel component will decrease.
- Both the perpendicular and the parallel component will increase.

#### 5.5 Simple Harmonic Motion

What physical characteristic of a system is its force constant related to?

- The force constant
*k*is related to the stiffness of a system: The larger the force constant, the stiffer the system. - The force constant
*k*is related to the stiffness of a system: The larger the force constant, the looser the system. - The force constant
*k*is related to the friction in the system: The larger the force constant, the greater the friction in the system. - The force constant
*k*is related to the friction in the system: The larger the force constant, the lower the friction in the system.

- A pendulum oscillates due to applied force.
- A pendulum oscillates due to the elastic nature of the string.
- A pendulum oscillates due to restoring force arising from gravity.
- A pendulum oscillates due to restoring force arising from tension in the string.

- It will increase because $g$ on the Moon is less than $g$ on Earth.
- It will decrease because $g$ on the Moon is less than $g$ on Earth.
- It will increase because $g$ on the Moon is greater than $g$ on Earth.
- It will decrease because $g$ on the Moon is greater than $g$ on Earth.