Physics

## 5.1Vector Addition and Subtraction: Graphical Methods

56 .
Find $\overrightarrow{\text{A}} - \overrightarrow{\text{B}}$ for the following vectors: $\overrightarrow{\text{A}} = (122\,\text{cm}, \angle\,145^\circ)$ $\overrightarrow{\text{B}} = (110\,\text{cm}, \angle\,270^\circ)$
1. 108 cm, $\theta = 119.0^\circ$
2. 108 cm, $\theta = 125.0^\circ$
3. 206 cm, $\theta = 119.0^\circ$
4. 206 cm, $\theta = 125.0^\circ$
57 .
Find $\overrightarrow{\text{A}} + \overrightarrow{\text{B}}$ for the following vectors: $\overrightarrow{\text{A}} = (122\,\text{cm}, \angle\,145^\circ)$ $\overrightarrow{\text{B}} = (110\,\text{cm}, \angle\,270^\circ)$
1. 108 cm, $\theta = 119.1^\circ$
2. 108 cm, $\theta = 201.8^\circ$
3. 232 cm, $\theta = 119.1^\circ$
4. 232 cm, $\theta = 201.8^\circ$
58.

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?

1. Zero
2. Six
3. Eight
4. Twelve
59.

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?

1. 0.0 N
2. 79.6 N
3. 82.8 N
4. 88.0 N

## 5.2Vector Addition and Subtraction: Analytical Methods

60.

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

1. True
2. False
61.

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

1. True
2. False
62 .
Consider $\overrightarrow{\text{A}} - \overrightarrow{\text{B}} = \overrightarrow{\text{R}}$. What is $R_x$ in terms of $A_x$ and $B_x$?
1. $R_x = \frac{A_x}{B_x}$
2. $R_x = \frac{B_x}{A_x}$
3. $R_x = A_x + B_x$
4. $R_x = A_x - B_x$
63 .
Consider $\overrightarrow{\text{A}} - \overrightarrow{\text{B}} = \overrightarrow{\text{R}}$. What is $R_y$ in terms of $A_y$ and $B_y$?
1. $R_y = \frac{A_y}{B_y}$
2. $R_y = \frac{B_y}{A_y}$
3. $R_y = A_y + B_y$
4. $R_y = A_y - B_y$
64.

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

1. Altitude
2. Heat
3. Temperature
4. Wind speed
65.

Which method is not an application of vector calculus?

1. To find the rate of change in atmospheric temperature
2. To study changes in wind speed and direction
3. To predict changes in atmospheric pressure
4. To measure changes in average rainfall

## 5.3Projectile Motion

66 .
How can you express the velocity, $\overrightarrow{v}$, of a projectile in terms of its initial velocity, $\overrightarrow{v_0}$, acceleration, $\overrightarrow{a}$, and time, $t$?
1. $\overrightarrow{v} = \overrightarrow{a}t$
2. $\overrightarrow{v} = \overrightarrow{v_0} + \overrightarrow{a}t$
3. $\overrightarrow{v} + \overrightarrow{v_0} = \overrightarrow{a}t$
4. $\overrightarrow{v_0} + \overrightarrow{v} + \overrightarrow{a}t$
67.

In the equation for the maximum height of a projectile, what does $v0y v0y$ stand for? $h= v 0y 2 2g h= v 0y 2 2g$

1. Initial velocity in the x direction
2. Initial velocity in the y direction
3. Final velocity in the x direction
4. Final velocity in the y direction
68.

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

1. True
2. False
69 .
For what angle of a projectile is its range equal to zero?
1. $0^\circ\!$ or $30^\circ$
2. $0^\circ\!$ or $45^\circ$
3. $90^\circ\!$ or $0^\circ$
4. $90^\circ\!$ or $45^\circ$

## 5.4Inclined Planes

70 .
What are the units of the coefficient of friction?
1. $\text{N}$
2. $\text{m/s}$
3. $\text{m/s}^2$
4. unitless
71 .
Two surfaces in contact are moving slowly past each other. As the relative speed between the two surfaces in contact increases, what happens to the magnitude of their coefficient of kinetic friction?
1. It increases with the increase in the relative motion.
2. It decreases with the increase in the relative motion.
3. It remains constant and is independent of the relative motion.
72 .
When will an object slide down an inclined plane at constant velocity?
1. When the magnitude of the component of the weight along the slope is equal to the magnitude of the frictional force.
2. When the magnitude of the component of the weight along the slope is greater than the magnitude of the frictional force.
3. When the magnitude of the component of the weight perpendicular to the slope is less than the magnitude of the frictional force.
4. When the magnitude of the component of the weight perpendicular to the slope is equal to the magnitude of the frictional force.
73 .
A box is sitting on a plane that can be tilted relative to the horizontal. At what angle (relative to the horizontal) is the perpendicular component of the box's weight at its maximum?
1. $0^\circ$
2. $30^\circ$
3. $60^\circ$
4. $90^\circ$

## 5.5Simple Harmonic Motion

74.

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

1. Amplitude
2. Deformation
3. Displacement
4. Restoring force
75.

What is the restoring force?

1. The normal force on the surface of an object
2. The weight of a mass attached to an object
3. Force which is applied to deform an object from its original shape
4. Force which brings an object back to its equilibrium position
76.

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

1. Mass only
2. Force constant only
3. Applied force and mass
4. Mass and force constant
77.

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

1. At the extreme positions
2. At the equilibrium position
3. At the moment when the applied force is removed
4. Midway between the extreme and equilibrium positions
78.

What is the equilibrium position of a pendulum?

1. When the tension in the string is zero
2. When the pendulum is hanging straight down
3. When the tension in the string is maximum
4. When the weight of the mass attached is minimum
79.

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

1. mgsinθ
2. mgcosθ
3. mgsinθ
4. mgcosθ