Review Exercise 2-2 Answers
Section 1: True-False
Indicate
whether the following statements are true or false by placing a check mark (P)
in the appropriate column.
|
Statement |
True |
False |
|
The speed of a falling object is not proportional to its mass or
weight |
P |
|
|
Mass refers to an object’s “quantity of matter” |
P |
|
|
Weight is a force |
P |
|
|
For a given force, the acceleration of an object is inversely
proportional to its mass |
P |
|
|
If only one non zero force acts on an object, it cannot have zero
acceleration |
P |
|
|
Acceleration is the rate of change of velocity |
P |
|
|
Acceleration can be negative |
P |
|
|
Velocity is the rate of change of distance with time |
P |
|
|
Newton’s first law deals with inertia |
P |
|
|
Newton’s third law equates force to mass times acceleration |
|
P |
|
Velocity is a scalar quantity |
|
P |
|
Acceleration and velocity are always in the same direction |
|
P |
|
A reference frame attached to an accelerating train is an inertial
reference frame |
|
P |
|
If the acceleration of an object is 0, there are no forces acting on
it |
|
P |
|
The normal force is always in the vertical direction |
|
P |
Section 2: Circle the Correct Answer
Part b:
Circle the correct answer; 1 correct answer for each
For each
of the following, circle the correct answer. There is only 1 correct answer
for each problem.
¢
Can work be done on a system if there is no motion?
a. Yes, if an outside force is provided.
b. Yes, since motion is only relative.
c. No, since a system which is not moving has no energy.
d. No, because of the way work is defined.
¢
A 50-N object was lifted 2.0 m vertically and is being held there.
How much work is being done in holding
the box in this position?
a. more than 100 J
b.100 J
c. less than 100 J, but more than 0 J
d. 0 J
¢ A truck weighs twice as much as a car, and is moving at twice the speed of the car. Which statement is true about the truck's kinetic energy compared to that
of the car?
a. All that can be said is that the truck has more kinetic energy.
b. The truck has twice the kinetic energy of the car.
c. The truck has 4 times the kinetic energy of the car.
d. The truck has 8 times the kinetic energy of the car.
¢ A brick is moving at a speed of 3 m/s and a pebble is moving at a speed of 5 m/s. If both objects have the same kinetic energy, what is the ratio of the brick's
mass to the rock's mass?
a. 25 to 9
b. 5 to 3
c. 12.5 to 4.5
d. 3 to 5
¢ A 4.0-kg mass is moving with speed 2.0 m/s. A 1.0-kg mass is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are
brought to rest.
Which object travels the greater
distance before stopping?
a. the 4.0-kg mass
b. the 1.0-kg mass
c. Both travel the same distance.
d. cannot be determined from the information given
¢ You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would
the car
have skidded, under the same conditions?
a. It would have skidded 4 times farther.
b. It would have skidded twice as far.
c. It would have skidded 1.4 times farther.
d. It is impossible to tell from the information given.
¢
A planet of constant mass orbits the Sun in an elliptical orbit.
Neglecting any friction effects, what happens to the
planet's kinetic energy?
a. It remains constant.
b. It increases continually.
c. It decreases continually.
d. It increases when the planet approaches the Sun, and decreases when it
moves farther away.
Section 3: Problems
Give answer (not just numbers in an equation) as a number with
appropriate units. If
p
is involved, leave it in your
answer.
¢
What is the magnitude of the momentum of a 28-g sparrow flying with a speed
of 8.4 m/s?
Simple
multiplication using the definition of momentum:
P = mb = (0.028 kg)(8.4 m/s) = 0.24 kg m/s
¢
A constant friction force of 25 N acts on a 65-kg skier for 20 s. What is
the skier’s change in velocity?
Use Newton's
second law in momentum form and solve for delta v
Assume the skier is moving to the right and let this be positive. The
friction then acts in a negative
direction
F = ma gives FD t = m D v gives D
v = F D t/m
Using the values given, we have D v = -(25 N)(20 s)/65 kg = -7.7 m/s
¢
A 1 kg ball is rotating uniformly at
the end of a string in a horizontal circle of 1 meter radius. It makes 1 revolution
per second.
ð
What is the period, T, of the ball?
The period is defined as the time taken for 1 complete revolution
The ball makes 1 rotation about the center in 1 second, therefore it makes 1
revolution in 1 second. So, T = 1 second.
ð
How fast
is the ball travelling?
Speed =
distance/time= 2
p
r/T = 2(3.14)(1)/1 = 2p m/s
=
6.28 m/s
ð
What is
the centripetal acceleration of the ball?
ar
= v2/r = (6.28)2/1 = 6.282 m/s2
¢
A
bike wheel rotates 4 revolutions. How many radians has it rotated?
(2
p
rad/rotation)x (4 rotations) = 8p
radians
¢ A person pulls a 10 kg box over a floor that has a coefficient of friction, Ffr, of 10 N. The box is pulled a straight line, horizontal distance of 20 m by a force of
30 N acting at an angle of
60 degrees.
Assume that the positive directions are up and to the right.
ð
What is the work done by the friction force, Wfr on the box?
Ffrxcosq
= (10)(20)cos180 = -200 J
ð
What is the work done by the person, WP, on the box?
FPxcosq
= (30)(20)cos45 = (30)20)(1/2) = 300 J
ð
What is the total work, WT, done on the box?
WT = Wfr +
WP = -200 J + 300 J
= 100 J
¢
A
disk is accelerated from rest to 60,000
revolutions per minute in 30 s.
ð
What is the angular velocity at the end of 30 s?
w
= 2p
f = (2
p
rad/rev) (60,000 rev/min)(min/60 sec) = 2000p
rad/s
¢
Assume
that the answer to the above question is m rad/sec. What is the average
angular acceleration during the
stated period?
ᾱ =
Dw/Dt
= (w
-
w0)/Dt
= (m - 0)/30 = m/30 rad/s2
¢ In the following drawing, two disk-shaped wheels of radii RA = 30 cm and RB = 50 cm (indicated by the horizontal and vertical lines from the center), are attached
to each other on an axle that passes through the center of each. Two forces are acting as shown. Calculate the net torque on this compound wheel due to the
forces shown.
We choose counterclockwise as positive, in accordance with convention.
¢
A long uniform rod has a mass of 2 kg and a length of 3 m. The axis is
through an end. What is the moment of
inertia of the rod.
(1/3) ML2 = (1/3)(2 kg)(3 m)2 = 6 kg m2
¢ A 3 kg sphere is rolling on a frictionless surface with an angular velocity of 4 rad/sec and a translational velocity of 2 m/sec. The moment of inertia of the sphere
is 2 kg m2. What s the total kinetic energy
of the object at a point in time?
KEtotal = KErotational + KEtranslational =
(1/2)mv2 + (1/2)Iw2
= (1/2)(3)(2)2 + (1/2)(2)(4)2
= 6 + 16 = 22
¢ A person is washing a car with a hose. Water leaves the hose at a rate of 2.0 kg/s with a speed of 20 m/s. The water is aimed at the side of the car which
stops it. Assume that there
is no splash back of
the water. What is the force
exerted by the water on the car?
Take the
positive direction to be to the right. Use Newton’s second law in momentum
form which is, in words
The
rate of change of momentum of an object is equal to the net force applied to
it
The
equation is
FDt
=
DP
When the
water hits the car the momentum goes to 0 (Pfinal = 0).
The
initial momentum of the water, Pinitial = mv = (2.0 kg/s)(20 m/s)
= 40.0 kg m/s.
Since
2.0 kg of water leaves the hose each second, we choose
Dt
= 1.0 s
FDt
=
DP
gives F =
DP/Dt
= (Pfinal – Pinitial)/1.0 s = 0 – 40 kg m/s
F = - 40
N which is the force exerted by
the car on the water. By
Newton’s third law, the force of the water on the car is equal to this with
opposite sign
F = 40 N
Section 4: Conservation Laws and Principles
Conservation laws are very important in physics; they allow us to solve
problems that would be difficult or impossible to solve without them.
It is important, however, to recognize when these laws are applicable
before they are used. A number of criteria (conditions that must be met in
order for the law to be applicable) are listed below and identified by the
characters A through G.
Criteria
For Use
A.
For collisions that are elastic
B.
In a system on which no outside
non-zero forces are acting
C.
In an inertial reference frame.
D.
In an inertial reference frame in
which there is no net force acting on the object.
E.
When the temperature is not too hot
F.
Always
G.
When only conservative forces are acting
H.
When the net torque acting on it is zero.
J.
When there is no torque acting on it.
K.
When the external forces acting on the system add to zero
M.
When there are no external forces acting on the system
¢
For each of the following
conservation laws or principles, place the appropriate criteria for its
use on the
adjacent line.
ð
Total
energy of a closed system
__________
F
ð
Newton's
first law of motion
__________
D
ð
Total
angular momentum of a rotating object.
__________
H
ð
Total
mechanical energy of an isolated system of objects
__________
G
ð
Total
kinetic energy of an isolated system of objects
__________
A
ð
Total
momentum of an isolated system of objects
__________
K
Section 5: Labs
A number
of labs, as listed below, were assigned. For each state the objective and
conclusion.
¢
Centripetal force lab.
To
measure the effect of speed on centripetal force. Theoretically, the
centripetal force should be directly proportional to the
square
of the speed. To check this, add a column to your data table for v2.
Construct a graph of centripetal force versus v2.
¢
Projectile slammed into a target on
an air table. After the collisions, the two remained
attached.
To
verify conservation of momentum in an inelastic collision.
¢
Ball rolling down different tracks.
To show
that the potential energy for balls on the different tracks is the same
because it depends on height, the same for all tracks. All of the potential
energy is converted into kinetic energy so the balls should travel about the
same distance (and they did).
Section 6: Demonstrations
A number
of demonstrations, as listed below were provided. They are included in the
Concepts Demonstrations By Chapter section of my manual. For each, identify
the principle or law, or concept that was being illustrated.
¢
Rotating rods of equal mass
Since I
is given by mr2, the rod with the mass near the center has a
lower I if rotated about the center.
If they are rotated about an end, however, the moments of inertia should be
about the same.
¢
Wheel and chair system
This is
an illustration of conservation of angular momentum.
¢
Ball being thrown by one student at
another
As Sir Isaac Newton explained,
åF
= ma = m
Dv/Dt
which leads to FDt
= m
Dv
=D
p where p is the momentum
FDt
is referred to as the impulse.
We can see that the impulse is directly related to the time (Dt)
over which the force acts.
Section 7: Answer the following questions.
¢
I
discussed and solved a problem in which a bullet struck a target suspended
by
a string. The
bullet lodged in the target which then swung up a given distance. I broke
the
problem into two
parts.
]
Why did I break the problem into 2 parts?
Because the same approach did not
work for both parts
]
What law or principle did I use for the first part?
Conservation of momentum since no net outside force was acting on the
system.
]
What law or principle did I use for the second part?
There was a net outside force acting (gravity) so conservation of momentum could not be used.
Conservation of mechanical energy could be used since
the only force acting was conservative (gravity)
¢ Define a radian as discussed in class and in the text. Just stating how many are in a circle or giving a relationship between a radian and a degree will receive no
credit.
A radian
is the angle subtended by an arc that is the same length as the radius of
the circle.
¢
A
disk is rotating at a constant angular velocity.
]
Does a point on the rim have radial or tangential acceleration or
both? Give clear and specific rationale for your answer.
Radial only.
aradial = rw
2 w
is a known constant,
w
¹
0
atan = r
Dw/Dt
Dw
= 0 (constant
w).
So atan = 0
]
If the disk’s angular velocity increases uniformly, does the point
have radial or tangential acceleration or both?
Give clear and specific rationale for your answer.
Both radial and tangential.
aradial = rw
2
w
is a known constant,
w
¹
0
atan = r
Dw/Dt
Dw
¹
0, so atan
¹
0
Section 8: Extra Credit
¢
Pictures and biographies of 10
giants in physics are listed on my Physics B home page. Identify the
following giants.
ð He assisted in the development of the atomic bomb and was a member of the panel that investigated the Space Shuttle Challenger disaster. In addition to his
work in theoretical physics, he has been credited with pioneering the field of quantum computing and introducing the concept of nanotechnology (creation of
devices at the
molecular scale.
ð He was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. __________________
Galileo Galilei
ð He was a German physicist and philosopher who, in 1925, discovered a way to formulate quantum mechanics in terms of matrices.____________________
Werner Heisenberg
ð Born in Copenhagen, Denmark. He won the 1922 Nobel prize for physics, chiefly for his work on atomic structure. ___________________ Niels Bohr