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Chapter 3

Practice Test 3

Educators


SECTION I - Problem 8

A car initially at rest accelerates linearly at a constant rate for eight
seconds. If the total displacement of the car was 600 m, what was the
speed of the car after the eight seconds of acceleration?
(A) 50 m/s
(B) 100 m/s
(C) 150 m/s
(D) 200 m/s

Kristela G.
Numerade Educator

SECTION I - Problem 29

The magnitude of the gravitation force between two objects is F. If the
distance between the two objects is tripled and the mass of one of the
objects is doubled, what is the new magnitude of the gravitation force
between the two objects?
(A) $\frac{1}{9} \mathrm{F}$
(B) $\frac{2}{9} \mathrm{F}$
(C) $\frac{1}{6} \mathrm{F}$
(D) $\frac{1}{4} \mathrm{F}$

Kristela G.
Numerade Educator

SECTION I - Problem 30

A mechanical wheel initially at rest on the floor begins rolling forward
with an angular acceleration of 2$\pi \mathrm{rad} / \mathrm{s}^{2}$ . If the wheel has a radius of $2 \mathrm{m},$ what distance does the wheel travel in 3 econds?
(A) 4$\pi \mathrm{m}$
(B) 6$\pi \mathrm{m}$
(C) 16$\pi \mathrm{m}$
(D) 18$\pi \mathrm{m}$

Kristela G.
Numerade Educator

Section 2 - Problem 1

Directions: Questions 1, 2, and 3 are short free-response questions that require about 13 minutes to answer and are worth 8 points. Questions 4 and 5 are long free-response questions that require about 25 minutes each to answer and are worth 13 points each. Show your work for each part in the space provided after that part.
The motion of an object is given by the following velocity-versus-time graph.
(a) What is the displacement of the object from time t = 0 s to t = 6 s in the graph above?
(b) At what times is the speed of the object increasing?
(c) Make of a sketch of the object’s position-versus-time graph during the time interval of t = 0 s to t = 6 s. Assume that the car begins at x = 0.

Kristela G.
Numerade Educator

Section 2 - Problem 2

Directions: Questions 1, 2, and 3 are short free-response questions that require about 13 minutes to answer and are worth 8 points. Questions 4 and 5 are long
free-response questions that require about 25 minutes each to answer and are
worth 13 points each. Show your work for each part in the space provided after that part.
A small box of mass m is placed on an inclined plane with an angle of incline of ?. There is a coefficient of kinetic friction ?k between the inclined plane and the small box. The small box is attached to a much heavier box of mass 3m by a pulley system shown below.
(GRAPH NOT COPY)
(a) Draw free body diagrams of both masses, including all of the forces acting on each.
(b) Assuming a frictionless, massless pulley, determine the acceleration of the blocks once they are released from rest in terms of $\mu_{k}, g,$ and $\theta .$
(c) If $\mu_{k}=0.3$ and $\theta=45^{\circ},$ what distance is traveled by the blocks 3 $\mathrm{s}$ after being released from rest?

Kristela G.
Numerade Educator

Section 2 - Problem 3

Directions: Questions 1, 2, and 3 are short free-response questions that require about 13 minutes to answer and are worth 8 points. Questions 4 and 5 are long free-response questions that require about 25 minutes each to answer and are worth 13 points each. Show your work for each part in the space provided after that part.
A cannon is used to launch a speaker emitting 3 kHz waves with a vertical velocity of 80 m/s. There is a stationary detector on the ground by the cannon.
(a) What is the frequency of the waves received by the detector 10 s after the speaker is launched?
(b) If the speaker begins simultaneous emitting 3.6 kHz waves, what will be the value of the beat frequency produced at the speaker?
(c) If the intensity of the sound received by the detector when the speaker reaches its maximum height is $8 \times 10^{-9} \mathrm{W} / \mathrm{m}^{2},$ what is the intensity received by the detector when the speaker is at half of its maximum height?

Kristela G.
Numerade Educator

Section 2 - Problem 4

Consider the following circuit:
(GRAPH NOT COPY)
(a) Determine the current that passes through $R_{3}$ and $R_{1}$ .
(b) At what rate does $R_{4}$ resistor dissipate energy?
(c) What is the voltage read by the voltmeter in the circuit?
(d) In order to minimize the impact of the voltmeter on the circuit, should the voltmeter have a very high or very low internal resistance?

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Section 2 - Problem 5

Two spheres (one hollow, one solid) are placed side by side on an inclined
plane and released at the same time. Both spheres roll down the inclined
plane without slipping.
(a) Using a free body diagram, explain what force provides the torque allowing the spheres to roll down the inclined plane.
(b) Which sphere reaches the bottom of the inclined plane first and why?
(c) How do the kinetic energies of the two spheres compare at the bottom of the inclined plane?

Kristela G.
Numerade Educator

SECTION I - Problem 1

A section of a river flows with a velocity of 1 m/s due S. A kayaker who
is able to propel her kayak at 1.5 m/s wishes to paddle directly east one
bank to the other. In what direction should she direct her kayak?
(A) $37^{\circ} \mathrm{N}$ of $\mathrm{E}$
(B) $42^{\circ} \mathrm{N}$ of $\mathrm{E}$
(C) $45^{\circ} \mathrm{N}$ of $\mathrm{E}$
(D) $48^{\circ} \mathrm{N}$ of $\mathrm{E}$

Kristela G.
Numerade Educator

SECTION I - Problem 2

If an object accelerates from $\mathbf{v}_{\mathbf{i}}=-\hat{\mathbf{i}}+4 \hat{\mathbf{j}}$ to $\mathbf{v}_{\mathbf{2}}=4 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}$ in $t$ seconds, what is the direction of its average acceleration relative to the $+x$ -x-axis?
(A) $50.2^{\circ}$
(B) $39.8^{\circ}$
(C) $-39.8^{\circ}$
(D) $-50.2^{\circ}$

Kristela G.
Numerade Educator

SECTION I - Problem 3

A student lives 1.2 km from school. On a particular day it takes her 10
min to get from home to school. Which of the following must be true
about this trip to school?
I. She travelled a distance of 1.2 km.
II. Her average speed was 2 m/s.
III. The magnitude of her average velocity was 2 m/s.
(A) I only
(B) II and III only
(C) III only
(D) I, II, and III

Kristela G.
Numerade Educator

SECTION I - Problem 4

In which of the following position-versus-time graphs does the object
in motion have a constant negative acceleration?
IMAGE CANNOT COPY

Kristela G.
Numerade Educator

SECTION I - Problem 5

In which section of the following velocity-time graph is the object
speeding up and moving in the negative direction?
(A) Section 1
(B) Section 2
(C) Section 3
(D) Section 4

Kristela G.
Numerade Educator

SECTION I - Problem 6

An airtanker is being used to fight a forest fire. It is flying with a ground speed of 85 m/s and maintaining an altitude of 300 m. If it is
flying directly towards the fire, at what approximate horizontal
distance from the fire should its tanks be open in order for the water
dropped to land on the fire? (Assume that the fire is relatively
localized.)
(A) 230 m
(B) 250 m
(C) 660 m
(D) 1700 m

Kristela G.
Numerade Educator

SECTION I - Problem 7

Two cannons are fired from a cliff at a height of 50 m from the
ground. Cannonball A is fired horizontally with an initial velocity of 40 m/s. Cannonball B is fired at a launch angle of 60° with an initial
velocity of 80 m/s. Which cannonball will have a greater magnitude of displacement after two seconds?
(A) Cannonball A
(B) Cannonball B
(C) Both cannonballs will have the same displacement.
(D) Cannot be determined

Kristela G.
Numerade Educator

SECTION I - Problem 9

A car travelling at a speed of v0 applies its breaks, skidding to a stop
over a distance of x m. Assuming that the deceleration due to the
breaks is constant, what would be the skidding distance of the same
car if the breaking were twice as effective (doubling the magnitude of deceleration)?
(A) 0.25x m
(B) 0.5x m
(C) x m
(D) 2x m

Kristela G.
Numerade Educator

SECTION I - Problem 10

A student is pushing a 3 -kg book across a table with a constant force of $30 .$ O $\mathrm{N}$ directed $10^{\circ}$ below the horizontal. The coefficient of kinetic friction between the book and the table is $0.3 .$ What is the magnitude of the force that the table exerts on the book during this motion?
(A) 30.7 N
(B) 36.1 N
(C) 38.2 N
(D) 45.0 N

Kristela G.
Numerade Educator

SECTION I - Problem 11

A box with a mass of 2 $\mathrm{kg}$ is placed on an inclined plane that makes a $30^{\circ}$ angle with the horizontal. What must the coefficient of static fraction $\left(\mu_{\mathrm{s}}\right)$ between the box and the inclined be in order for the box to be at rest?
(A) 0.5
(B) 0.58
(C) 0.87
(D) 1

Kristela G.
Numerade Educator

SECTION I - Problem 12

A construction worker strikes a nail with a hammer twice with the
same initial velocity $\left(v_{1}\right) .$ The first time, the hammer comes to rest after hitting the nail. The second time, the hammer recoils after hitting the nail and bounces back toward the worker. Assuming the contact time in both strikes is the same, in which strike did the nail exert a greater force on the hammer?
(A) The first strike
(B) The second strike
(C) The nail exerted the same force for both strikes.
(D) Cannot be determined

Kristela G.
Numerade Educator

SECTION I - Problem 13

A box with a mass of 5 $\mathrm{kg}$ is sliding across a table at a speed of 2 $\mathrm{m} / \mathrm{s}$ . The coefficient of kinetic friction between the book and table is $\mu=$ $0.25 .$ What is the minimum force that has to be applied on the box to maintain this speed?
(A) oN
(B) 10 $\mathrm{N}$
(C) 12.3 $\mathrm{N}$
(D) 24.6 $\mathrm{N}$

Kristela G.
Numerade Educator

SECTION I - Problem 14

Two students each push a 30 kg box across the room. Student A
applies a constant force of 30 N. Student B starts with a force of 40 N
but gradually reduces the force due to fatigue. Given the force-versus- position graphs of the two students, at what position have both students done the same amount of work?
(A) 2 $\mathrm{m}$
(B) 3 $\mathrm{m}$
(C) 4 $\mathrm{m}$
(D) 5 $\mathrm{m}$

Kristela G.
Numerade Educator

SECTION I - Problem 15

A 2000 kg is initially traveling with a speed of 20 m/s. The driver applies the break and the truck slows to 10 m/s. How much work was done by the frictional force applied from the breaks?
(A) –10,000 J
(B) –5,000 J
(C) 5,000 J
(D) 10,000 J

Kristela G.
Numerade Educator

SECTION I - Problem 16

A box of mass $m$ slides down a frictionless inclined plane of length $L$ and height $h .$ If the box is initially at rest, what is the speed of the box halfway down the inclined plane?
(A) $\sqrt{2 g h}$
(B) $\sqrt{g h}$
(C) $\sqrt{\frac{g h}{2}}$
(D) $\frac{g h}{4}$

Kristela G.
Numerade Educator

SECTION I - Problem 17

A car with a mass of 1000 kg experiences a frictional force of 3500 N
while driving at a constant speed of a 15 m/s. What is the power
output of the car’s engine?
(A) 3.5 kW
(B) 5.25 kW
(C) 35.0 kW
(D) 52.5 kW

Kristela G.
Numerade Educator

SECTION I - Problem 18

A student launched a small rocket with a mass of 50 kg into the air
with an initial velocity of 10 m/s in the positive vertical direction. The
student then turns on the secondary engines of the rocket to apply a
constant upwards force that increases the velocity of the rocket to 15
m/s. If the force provided by the secondary engines did 2,000 J of
work, how much work did the force of gravity do on the rocket?
(A) $-500 \mathrm{J}$
(B) $-750 \mathrm{J}$
(C) $-1,25$ O $J$
(D) $-1,5$ OO $J$

Kristela G.
Numerade Educator
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