Test Prep

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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

A plane flies north at

200 m/s

with a headwind blowing from the north at

70 m/s

. What is the resultant velocity of the plane?

$130 m/s$ north
$130 m/s$ south
$270 m/s$ north
$270 m/s$ south

Two hikers take different routes to reach the same spot. The first one goes

255 m

southeast, then turns and goes

82 m

14^{\circ}

south of east. The other goes

200 m

south. How far and in which direction must he travel now, in order to reach his destination?

$200 m$ east
$200 m$ south
$260 m$ east
$260 m$ south

5.2 Vector Addition and Subtraction: Analytical Methods

When will the x-component of a vector with angle

θ

be greater than its y-component?

$0^{\circ} < θ < 45^{\circ}$
$θ = 45^{\circ}$
$45^{\circ} < θ < 60^{\circ}$
$60^{\circ} < θ < 90^{\circ}$

The resultant vector of the addition of vectors

\vec{a}

and

\vec{b}

\vec{r}

. The magnitudes of

\vec{a}

\vec{b}

, and

\vec{r}

are

A

B

, and

R

, respectively. Which of the following is true?

$R_{x} + R_{y} = 0$
$A_{x} + A_{y} = \vec{A}$
$A_{x} + B_{y} = B_{x} + A_{y}$
$A_{x} + B_{x} = R_{x}$

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

Which is true when the height of a projectile is at its maximum?

$v_{y} = 0$
$v_{y} = maximum$
$v_{x} = maximum$

10.

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

11.

A large rock is ejected from a volcano with a speed of

30 m/s

and at an angle

60^{\circ}

above the horizontal. The rock strikes the side of the volcano at an altitude of

10.0 m

lower than its starting point. Calculate the distance traveled by the rock.

$84.90 m$
$96.59 m$
$169.80 m$
$193.20 m$

5.4 Inclined Planes

12.

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

13.

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

14.

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.

15.

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

16.

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

Velocity
Length
Mass
Weight

17.

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

Speed
Displacement
Acceleration
Force

18.

Up to approximately what angle is simple harmonic motion a good model for a pendulum?

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

19.

How would simple harmonic motion be different in the absence of friction?

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.

20.

What mass needs to be attached to a spring with a force constant of

7 N/m

in order to make a simple harmonic oscillator oscillate with a time period of

3 s

$0.03 kg$
$1.60 kg$
$30.7 kg$
$63.0 kg$

Short Answer

5.1 Vector Addition and Subtraction: Graphical Methods

21.

Find

\vec{A} - \vec{B}

for the following vectors:

\vec{A} = (122 cm, ∠ 145^{\circ})

\vec{B} = (110 cm, ∠ 270^{\circ})

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

22.

Find

\vec{A} + \vec{B}

for the following vectors:

\vec{A} = (122 cm, ∠ 145^{\circ})

\vec{B} = (110 cm, ∠ 270^{\circ})

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

23.

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

24.

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

25.

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

True
False

26.

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

True
False

27.

Consider

\vec{A} - \vec{B} = \vec{R}

. What is

R_{x}

in terms of

A_{x}

and

B_{x}

$R_{x} = \frac{A_{x}}{B_{x}}$
$R_{x} = \frac{B_{x}}{A_{x}}$
$R_{x} = A_{x} + B_{x}$
$R_{x} = A_{x} - B_{x}$

28.

Consider

\vec{A} - \vec{B} = \vec{R}

. What is

R_{y}

in terms of

A_{y}

and

B_{y}

$R_{y} = \frac{A_{y}}{B_{y}}$
$R_{y} = \frac{B_{y}}{A_{y}}$
$R_{y} = A_{y} + B_{y}$
$R_{y} = A_{y} - B_{y}$

29.

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

Altitude
Heat
Temperature
Wind speed

30.

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

31.

How can you express the velocity,

\vec{v}

, of a projectile in terms of its initial velocity,

\vec{v_{0}}

, acceleration,

\vec{a}

, and time,

t

$\vec{v} = \vec{a} t$
$\vec{v} = \vec{v_{0}} + \vec{a} t$
$\vec{v} + \vec{v_{0}} = \vec{a} t$
$\vec{v_{0}} + \vec{v} + \vec{a} t$

32.

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

h = \frac{v_{0} {_{y}}^{2}}{2 g}

Initial velocity in the x direction
Initial velocity in the y direction
Final velocity in the x direction
Final velocity in the y direction

33.

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

True
False

34.

For what angle of a projectile is its range equal to zero?

$0^{\circ}$ or $30^{\circ}$
$0^{\circ}$ or $45^{\circ}$
$90^{\circ}$ or $0^{\circ}$
$90^{\circ}$ or $45^{\circ}$

5.4 Inclined Planes

35.

What are the units of the coefficient of friction?

$N$
$m/s$
${m/s}^{2}$
unitless

36.

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?

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.

37.

When will an object slide down an inclined plane at constant velocity?

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.

38.

A box is sitting on an inclined plane. At what angle of incline is the perpendicular component of the box's weight at its maximum?

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

5.5 Simple Harmonic Motion

39.

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

Amplitude
Deformation
Displacement
Restoring force

40.

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

41.

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

42.

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

43.

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

44.

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

mgsinθ
mgcosθ
–mgsinθ
–mgcosθ

Extended Response

5.1 Vector Addition and Subtraction: Graphical Methods

45.

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

True
False

46.

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

47.

For which angles of a vector is it possible that its magnitude will be equal to its y-component?

$θ = 0^{\circ}$
$θ = 45^{\circ}$
$θ = 60^{\circ}$
$θ = 90^{\circ}$

48.

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

True
False

49.

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

50.

Ignoring drag, what is the x-component of the acceleration of a projectile? Why?

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.

51.

What is the optimum angle at which a projectile should be launched in order to cover the maximum distance?

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

5.4 Inclined Planes

52.

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

True
False

53.

As the angle of the incline gets larger, what happens to the magnitudes of the perpendicular and parallel components of gravitational force?

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

54.

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.

55.

How or why does a pendulum oscillate?

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.

56.

If a pendulum from earth is taken to the moon, will its frequency increase or decrease? Why?

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.

Test Prep

Multiple Choice

5.1 Vector Addition and Subtraction: Graphical Methods

5.2 Vector Addition and Subtraction: Analytical Methods

5.3 Projectile Motion

5.4 Inclined Planes

5.5 Simple Harmonic Motion

Short Answer

5.1 Vector Addition and Subtraction: Graphical Methods

5.2 Vector Addition and Subtraction: Analytical Methods

5.3 Projectile Motion

5.4 Inclined Planes

5.5 Simple Harmonic Motion

Extended Response

5.1 Vector Addition and Subtraction: Graphical Methods

5.2 Vector Addition and Subtraction: Analytical Methods

5.3 Projectile Motion

5.4 Inclined Planes

5.5 Simple Harmonic Motion

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