Download Final Exam from Fall 2001

Final Exam
Dec. 18, 2001
Physics 211 Fall 2001
Name_________________________
This final exam consists of several questions, each with several parts. If you cannot do one part,
move on to the next. Partial credit will be given on all parts of this exam.
This is a closed book exam. You will need a calculator. Please remember to write your name
above, and on every page.
To receive full credit, you must show all your reasoning. Remember that arrows are a great aid
in reasoning and that relying on plus and minus signs can be tedious and dangerous! Correct
answers are not enough, and if fact, less important than your reasoning. Do not worry too much
about errors in calculation, as I will look more for your understanding of, and your ability with,
the concepts. Do not use the “kinematic equations” from the text. All problems can be solved
with the concepts and equations given on the front sheet. Please ask if the wording of a question
is not clear to you.
If you do not know where to start, do something and comment on the reasonableness of your
result. It may help to write down what you intend to do before you do it.
Please write your name on every page.
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Final Exam
Dec. 18, 2001
Physics 211 Fall 2001
Name_________________________
1) [30 points total] Of the following only e) and f) are related to each other. Be sure to show
how you arrived at your conclusion, that is, show your reasoning. Let g = 10N/kg.
a) [5 points] The forces on the meter
stick are drawn to scale. Determine if
it is in equilibrium. That is, are Fnet
and net both zero? Show how you
know.
b) [5 points] A car travels 90m while
coming to rest. Initially its velocity
is 60m/s north. Find the magnitude
and direction of the acceleration.
Show your reasoning.
d) [5 points] Two balls are thrown
from the top of a building at the
same initial speed but one is thrown
horizontal and the other is thrown
toward the ground at an angle of 45
below the horizontal. Which, if
either, hit the ground with a greater
final velocity? Show your reasoning.
e) [5 points] A 40N rocket engine is
attached to a 10kg rocket sled. The
coefficients of static and kinetic
friction are 0.6 and 0.5 respectively
(between the sled and the floor).
Does the sled move? Explain.
c) [5 points] A ring and disk both
rolling at the same initial velocity
roll without slipping up a ramp.
Which one, if either goes higher?
Show your reasoning.
f) [5 points] What is the size of the
friction force the floor puts on the
sled in question e)? Show your
reasoning.
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Final Exam
Dec. 18, 2001
Physics 211 Fall 2001
Name_________________________
2) [15 points total] A compressed spring is tied between two hockey pucks. A gerbil sitting on
one puck cuts the string, allowing the spring to expand. Initially the system moves to the
right with velocity v but when the string is cut the puck with the gerbil on it come to rest.
The mass of the gerbil is m and the mass of each puck is also m and the surface is
frictionless.
vsys
v=0
v=?
a) [8 points] Assume the spring puts the same size force on either puck. Find the final
velocity of single puck. Show all of your reasoning (draw arrows).
Now the single puck returns with the same velocity found in part a) and collides and sticks to
the puck with the gerbil, which is still at rest. The spring is gone and is no longer involved.
b) [7 points] Find the final velocity of the system (two pucks and a gerbil) after the
collision. Show your reasoning (draw arrows).
3) [15 points total] A steamroller is made from two rings and a frame, all of mass m. A tension
force T pulls the steamroller a distance x.
a) [5 points] Find the fraction of the total
T
kinetic energy in rotation and translation as the
steamroller rolls without slipping.
m
m
Rings
m
b) [10 points] Find the acceleration of the steamroller. Express your answer in terms of T
and m. Show your reasoning.
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Final Exam
Dec. 18, 2001
Physics 211 Fall 2001
Name_________________________
4) [30 points total] A hand pushes two blocks across a rough
table. Block A’s mass is 8kg and that of B is 4kg. The
blocks are moving left and speeding up with acceleration
2m/s2. Let g = 10N/kg.
a) [10 points] Draw free body
diagrams of both blocks
showing all forces acting on
them, labeled as in class.
Identify any 3rd law pairs.
Include the directions of a
and Fnet as given above.
a=
Fnet=
B
B
A
a=
Fnet=
A
b) [5 points] The friction force on block B is 15N. Find the normal force that A puts on B.
Show your reasoning.
c) [5 points] Find the force the hand puts on block A. Show your reasoning.
d) [5 points] The friction forces disappear but the hand continues to push with the same
force. Find the acceleration of the blocks.
e) [5 points] What is the normal force that B puts on A now? Show your reasoning.
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Final Exam
Dec. 18, 2001
Physics 211 Fall 2001
Name_________________________
5) [15 points total] A mass and spring system is assembled in
the vertical position as shown. All dimensions are drawn to
scale and buckets are provided as an aid to your reasoning.
Note that the amplitude of the oscillation equals one-half
the equilibrium stretch, xeq. Let g = 10N/kg.
a) [5 points] There are 20J of energy in the spring at the
equilibrium position. How many joules are in the
spring when the mass is at its highest and lowest points?
Show your reasoning. Hint: Use proportional
reasoning.
xeq
A
A = 1/2xeq
20
K S g
0
0
K S g
b) [5 points] If the spring constant is 1000N/m,
what is the amplitude and the mass? Show your reasoning.
c) [5 points] Find the velocity of the mass as it passes
the equilibrium position. Show your reasoning.
6) [15 points total] A block slides off of a table
with an initial horizontal velocity of 20m/s.
It lands 10m from the base of the table. Let
g = 10N/kg.
20m/s
10m
a) [10 points] Find the final velocity of the block (magnitude and direction),
just before it hits the floor. Show your reasoning.
b) [5 points] How high is the table? Show your reasoning.
5
0
K S g
Final Exam
Dec. 18, 2001
Physics 211 Fall 2001
Name_________________________
7) [15 points total] A mass on a 2m string swings
down from rest from the position shown.
Let g = 10N/kg.
v=0
2m
a) [8 points] Find the acceleration (magnitude and
direction) of the mass the instant it is at the
lowest point. Show your reasoning.
b) [7 points] Find the tension in the string. Show your reasoning.
v
8) [15 points total] Two balls with mass m and 2m collide as
shown. Both balls begin with the same velocity, v, and then
the small ball moves with velocity v in the direction shown.
a) [10 points] Find the final velocity (magnitude and
direction) of large ball. Show your reasoning including
momentum arrows.
velocity?
direction?
v
m
v
2m
b) [5 points] Is the collision elastic? Show your reasoning.
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