PHYS 211 – Final Exam Fall 2012 Sample 2

PHYS 211 – Final Exam
Fall 2012
Sample 2
1) A waiter is in an elevator, holding a stack of dishes. As observed by someone
standing still on the ground floor, watching the elevator move down towards them with
constant speed, what is the sign of the work done by the uppermost dish on the one
directly below it?
A. Positive
B. Negative
C. Zero
2) The figure below shows the relation between position x and time t for a particle.
Which of the following statements are true?
1.
2.
3.
4.
5.
6.
The particle's velocity is negative at a.
The particle's acceleration is zero at a.
The particle's acceleration is negative at f.
The particle's velocity is negative at b.
The particle's acceleration is roughly zero at c.
The particle's velocity is zero at c.
A.
B.
C.
D.
E.
1, 2, 6
3, 4, 5
4, 6
2, 3, 4
2, 5
PHYS 211 – Final Exam
Fall 2012
Sample 2
3) A particle is in simple harmonic motion with period T. At time t = 0 it is halfway
between the equilibrium point and an end point of its motion, traveling toward the end
point. The next time it is at the same place is:
A. t = T
B. t = T/2
C. t = T/4
D. t = T/8
E. none of the above
4) As you are leaving a building, the door opens outward. If the hinges on the door are
on your right, what is the direction of the angular velocity of the door as you open it?
A. up
B. down
C. to your left
D. to your right
E. forwards
5) A bomber flying in level flight with constant velocity releases a bomb before it is over
the target. Neglecting air resistance, which one of the following is NOT true?
A. The bomber is over the target when the bomb strikes.
B. The acceleration of the bomb is constant.
C. The horizontal velocity of the plane equals the vertical velocity of the bomb when
it hits the target.
D. The bomb travels in a curved path.
E. The time of flight of the bomb is independent of the horizontal speed of the plane.
PHYS 211 – Final Exam
Fall 2012
Sample 2
6) A man, holding a weight in each hand, stands at the center of a horizontal
frictionless rotating turntable. The effect of the weights is to double the rotational inertia
of the system. As he is rotating, the man opens his hands and drops the two weights.
They fall outside the turntable.
Then:
A.
B.
C.
D.
E.
his angular velocity doubles.
his angular velocity remains about the same.
his angular velocity is halved.
the direction of his angular momentum vector changes.
his rotational kinetic energy increases.
7) A block attached to a spring oscillates in simple harmonic motion along the x axis.
The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these
extremes to the other in 0.25 s. Its amplitude and frequency are:
A.
B.
C.
D.
E.
40 cm, 2 Hz
20 cm, 4 Hz
60 cm, 2 Hz
25 cm, 4 Hz
20 cm, 2 Hz
8) A ball is released from rest on a no-slip surface,
as shown in the figure. After reaching its lowest
point, the ball begins to rise again, this time on a
frictionless surface as shown in the figure. When the
ball reaches its maximum height on the frictionless
surface, it is
A.
B.
C.
D.
at a greater height as when it was released.
at a lesser height as when it was released.
at the same height as when it was released.
It is impossible to tell without knowing the
mass of the ball.
E. It is impossible to tell without knowing the radius of the ball.
PHYS 211 – Final Exam
Fall 2012
Sample 2
9) A socket wrench hangs off of a bolt as shown
below with  = 30.°. The wrench's mass is 1.0 kg
and its center of mass is 0.10 m from the center of
the bolt. The arrow shows a 4.0 N force which is
perpendicular to the wrench being applied 0.25 m
from the center of the bolt.
About what is the net torque acting on the wrench?
A. 1 N∙m out of page
B. 0
C. 0.5 N∙m out of page


D. 1  12 3 N∙m out of page
E. None of the above
10) Consider a cylindrical toy which can switch from having its mass roughly equally
distributed across its cross-section (solid cylinder) to having its mass concentrated at its
outer edge (hollow cylinder). With the toy spinning on frictionless bearings around its
central symmetry axis, you push a button and it converts from “solid” to “hollow” mode.
What happens to its rotational kinetic energy?
A.
B.
C.
D.
E.
Increases by a factor of 4
Increases by a factor of 2
Stays the same
Decreases by a factor of 2
Decreases by a factor of 4
PHYS 211 – Final Exam
Fall 2012
Sample 2
11) A horizontal uniform wooden board is balanced on two big triangles which are 4
meters apart as shown below. The board is 6 meters long with weight of 1000 Newtons
as shown in the figure below. What is the magnitude of the force on the board from the
triangle which is 2 meters from the right edge of the board?
A.
B.
C.
D.
E.
1000 N
750 N
500 N
400 N
250 N
12) A simple pendulum has length L and period T. As it passes through its equilibrium
position, the string is suddenly clamped at its midpoint. The period then becomes:
A.
B.
C.
D.
E.
2T
T
T/2
T/4
none of these
PHYS 211 – Final Exam
Fall 2012
Sample 2
13) A square board of mass M
(uniformly distributed across its area)
hangs from a string at its center.
Forces of magnitude F2 pull
downwards on two adjacent corners
as shown. The force F1 is applied to
the opposite edge of the board in the
center of the edge. The system
experiences the Earth's gravity.
As part of a lab assignment you are
asked to determine how large F1 must
be in order for the system to be in
static equilibrium and how you know
this to be the case.
A. F1 = 2F2 because the net force
on the plate must be zero
B. F1 = 2F2 because the force at the back of the plate (causing the front edge to
rise) must cancel out the force at the front edge (causing it to drop)
C. F1 = 2 2 F2 because the torque from F1 must be equal and opposite the
combined torques from the F2s (note they are
D. F1 =
2 farther away)
2 F2 because the torque from F1 must be equal and opposite the combined
torques from the F2s (note they are
each other
E. None of the above
2 farther away) but half their torques cancel
PHYS 211 – Final Exam
Fall 2012
Sample 2
2
14) The velocity of an object is given by the expression v(t) = 3.00 m/s + (4.00 m/s3)t .
Determine the position of the object as a function of time if it is located at x = 1.00 m at
time t = 0.000 s.
A.
B.
C.
D.
E.
(4.00 m/s)t + 1.00 m
(3.00 m/s)t + (1.33 m/s3)t3
(4.00 m/s)t
1.33 m
3
1.00 m + (3.00 m/s)t + (1.33 m/s3)t
15) A 4.0 kg brick slides on a frictionless floor at 2.0 m/s in the positive y-direction. A
sticky piece of putty with a mass of 1.0 kg slides at 6.0 m/s in the negative x-direction.
The two collide and stick together. What is the speed of the brick-putty mass after the
collision?
A.
B.
C.
D.
E.
0.4 m/s
2.0 m/s
2.8 m/s
10 m/s
None of the above
16) Your roommate is trying to solve the following problem:
"A solid uniform disc of mass M and radius R has an axle through its center, around
which it can rotate freely. A string is wrapped around the edge of disc. On the other end
of the string hangs a mass m. What is the tension T in the string after the mass is
allowed to fall?"
When your roommate put the answer in MasteringPhysics, however, it was marked
wrong. You agree to take a look at your roommate's work, which is shown below.
(These are just the equations that describe the situation - you trust your roommate to do
the algebra correctly.) You find one error and say that it's on line:
(A) I = ½ MR2
(B)  = -TR
(C) T = maz
(D) -TR = I
(E) az = r
PHYS 211 – Final Exam
Fall 2012
Sample 2
17) A pulley with radius R and moment of inertia I is
free to rotate around a horizontal fixed axis through its
center. A string passing over the pulley is attached to
m1 on one end and m2 on the other. You observe m1 is
moving downward with speed v. If the string does not
slip on the pulley, what is the approximate magnitude of
the total angular momentum of the masses and pulley,
taken around the pulley axis?
A.
B.
C.
D.
E.
|(m1 - m2)vR + Iv/R|
|(m1 + m2)vR + Iv/R|
|(m1 - m2)vR - Iv/R|
|(m1 + m2)vR - Iv/R|
none of the above
18) A mass M is connected to a spring with spring constant k, and it is oscillating with a
period T. If 45 kg is added to the original mass, the period is found to quadruple. The
original mass, M, is:
A.
B.
C.
D.
E.
9 kg
5 kg
3 kg
6 kg
1.5 kg
PHYS 211 – Final Exam
Fall 2012
Sample 2
19) A uniform, thin rod with mass 12 kg and length 50. cm has a frictionless, horizontal
axle through one end. If the rod is held horizontally as shown and then released from
rest, what is the initial angular acceleration of the rod (measured about the axle)? Make
the approximation (as always) that g = 10 m/s2
A.
B.
C.
D.
E.
10 rad/s2
30 rad/s2
60 rad/s2
120 rad/s2
240 rad/s2
20) A heavy ball of putty (mass m=0.50 kg,
speed v0=10 m/s) is thrown at a block of wood
(mass M=1.0 kg) which hangs at rest from a
cord. The putty sticks to the wood. In the figure,
snapshots show the system just before the
putty hits, and later, when the putty/block
system has just come to a halt at the high point
of its swing.
Before
v0
m
M
After
m+M
In the "after" picture, the center of mass of the whole system has risen a height "h".
What is h? (Use g = 10 m/s2)
A. 0.56 m
B. 1.7 m
C. 2.5 m
D. 5.0 m
E. 10. m
h
PHYS 211 – Final Exam
Fall 2012
Sample 2
21) A hand pushes horizontally with a constant force on a physics book,
holding it up against a wall. Nothing is moving.
The coefficient of static friction between the wall and book is s.
However, there is zero static friction between the hand and the book.
s
F(hand)
If the hand suddenly increases its horizontal push to TWICE what it was
before, what happens to the frictional force of the wall on the book?
A. It doubles
B. It increases by more than a factor of 2
C. It increases, but by less than a factor of 2.
D. It decreases.
E. It stays exactly the same
22) A cart is moving with a constant horizontal velocity of 5 m/s. A small pebble (of
negligible mass) is launched from the front of the cart with a velocity of 10 3 m/s at
60.0° above the horizontal as measured relative to the cart (see figure) and experiences
no significant air resistance. Using the approximation that g = 10 m/s2, just as the
pebble returns to the level from which it was launched, its distance from the front of the
cart is closest to
10 3 m/s
5 m/s

B) 15 
A) 15

3  1 m.
3  1 m.
C) 10 3 m.
D) 15 3 m.
E) 20 3 m.
PHYS 211 – Final Exam
Fall 2012
Sample 2
23) A friend is asked to solve the following problem:
“A block of unknown mass is dropped onto a spring with a spring constant k = 1000 N/m
from a height h = 20 cm above the uncompressed end of a spring. Assuming that the
equilibrium position, once the block comes to rest, will be a distance x = 10 cm below
the uncompressed length, find the maximum distance (from the uncompressed position)
that the spring is compressed as the mass lowers to an eventual brief halt.”
Indicate which of the steps he took below is incorrect, if any, in the solution to the
problem. You do not need to check the mathematics and you should assume all
mathematical calculations are correct. Just check for possible conceptual errors.
He of course started by drawing pictures (a schematic and an FBD), which he did
perfectly, but which is not reproduced here
A. First we determine the mass of the block. The equilibrium length is where the
force of gravity equals the spring force:
mg  kx
B. Solve for the mass
m
kx 1000N/m  0.1m 

 10 kg
g
10 sm2 
C. Next, write the conservation of energy equation: (Potential energy @ top = spring
energy @ bottom):
mgh  12 k  s 
2
D. Solve for the distance of the compression. This is the distance from the
uncompressed length, NOT from the equilibrium length, so it is what we want:
s 
2 10kg  10 sm2   0.2m 
2mgh
4


m  20cm
k
100
1000 N/m 
E. All steps are correct.
PHYS 211 – Final Exam
Fall 2012
Sample 2
24) A mass moves on a frictionless plane. It is attached to a string (length r) and is
swinging about the origin with constantly increasing angular velocity. At time t = 0 s it is
moving with velocity vjˆ and has a linear acceleration pointing 45 degrees above the –x


axis in the ˆi  ˆj direction. From this point in time how long will you have to wait for its
speed to double?
A. r v
B. 2r v
C. 2 r v
D. It is impossible to know with the given information
E. None of the above
25) A swimmer heads directly across a river 300 m wide. A person with a radar gun
stands 400 m downstream on the opposite bank and sees the swimmer heading straight
at them at 1 m/s. How fast is the river flowing?
A.
B.
C.
D.
E.
1 m/s
0.8 m/s
0.6 m/s
Not enough information to determine
None of the above