PHYS 1104 page 1 of 9 Dec. 9, 2011
Final Exam
Cape Breton University Fall 2011 Dec. 9, 2011
PHYS 1104 Final Exam
Place your name on the top of this sheet immediately.
Please do not open the exam until instructed to do so.
Warning: Statistical mechanics tells us that there is a very small probability
that all of the molecules of air in the room could end up in one half of the
room. Should this occur, anyone in the other half of the room would suffer
violent decompression leading to serious injury. While the probability of
this event is so small that there aren't enough particles in the visible
universe to write the probability in full, we cannot absolutely guarantee that
it will not happen. The makers of this exam cannot be held responsible for
such an unfortunate event.
Aids allowed:
•writing implements (pencil recommended)
•calculator (graphing or programmable OK)
•straightedge
•a paper English/[Language of your choice] dictionary
•8.5 X 11 in., single-sided, hand-written “cheat sheet”
•your brain (If you've forgotten it then borrow one. You'll need it!)
Start time: 9:00
End time: 12:00
Time limit: 180 minutes (3 hours)
Page count (including this one): 10
This exam consists of 8 short answer questions and 6 long problems. Budget
your time accordingly. You may write on the backs of pages if you run out of
space, but please indicate where you have done this so that I don’t miss it. Neatly
cross out things that you consider incorrect rather than erasing them. This way I
can give you part marks for them if they are, in fact, correct.
Total marks on exam: XXXXXXXXXXBONUS
This exam counts for 30% of your final mark in the course.
Feel free to use g = 10.0 m/s2
PHYS 1104 page 2 of 9 Dec. 9, 2011
Final Exam
Short answer questions:
Each of the following questions, or question parts should be answerable in a few (1-3) sentences and/or a diagram.
Point form answers are acceptable as long as they are clear. No calculations are required.
S1. For each of the following collisions say whether you think momentum is approximately conserved and why and
whether you think energy is approximately conserved and why.
a) A neutron hits a Uranium nucleus and is absorbed by it. [2 marks]
Momentum conserved? Energy conserved?
Explanation: Explanation:
b) A ship collides with another ship. Both ships engines generate thrust throughout the collision and the collision
takes about 10 s to be completed. [2 marks]
Momentum conserved? Energy conserved?
Explanation: Explanation:
S2. A resourceful child (who probably won't live to see his 10th birthday...) has got his
hands on a large signal flare rocket. He has duct taped it to the back of his sled and
ignited it for a fun ride on the icy streets. As shown in the diagram at right, at some
moment towards the end of the ride he passes through point A going quite fast. Some
time later he passes through B at some speed which is slower than at A (the rocket is still going but it providing less
thrust by this time which is why he is slowing down). Suppose we want to find the speed at B.
a) Draw the energy bar graph for this situation. Define your system as the child, the sled, the Earth and the slope.
Friction is not negligible. [4 marks]
b) Draw the energy bar graph again but this time define your system as the child, the sled and the Earth. [4 marks]
PHYS 1104 page 3 of 9 Dec. 9, 2011
Final Exam
S3. Two identical blocks, each of the same mass, M, are pulled across a rough surface using ropes. Each is pulled
at constant speed. However block A is pulled at speed, v, while block B is pulled at speed 2v. Air drag is negligible.
Compare the tensions, TA and TB, in the ropes connected to the two blocks. Explain. [2 marks]
S4. Now two blocks, one of mass M and the other of mass 2M are pulled across a frictionless floor. Each is pulled
by the same force, F. They both start at rest.
a) Suppose they are pulled for the same distance. Which will have the greater kinetic energy? Explain. [2 marks]
b) Again supposing they are pulled for the same distance, which will have the greater momentum? Explain. [2
marks]
S5. Three balls are thrown from exactly the same height with exactly the same speed. Ball a is thrown upward, ball
b is thrown horizontally and ball c is thrown down.
a) Rank the final speeds of the balls at the instants when they hit the ground. Explain your
ranking. [2 marks]
b) Rank the final vertical components of velocity of the balls at the instants when they hit
the ground. [2 marks]
S6. An express elevator is accelerating upward. A parcel is sliding to the right across the floor.
a) Is the elevator an inertial reference frame? Explain how you know. [2 marks]
b) Draw a free body diagram for the parcel. Don't forget to indicate the direction of the net force. [3 marks]
PHYS 1104 page 4 of 9 Dec. 9, 2011
Final Exam
S7. Trogdor the Burninator moves in a big “V” shape as shown in the
motion diagram at right. The labels on points indicate seconds from the
start of the motion.
a) Add acceleration vectors to the motion diagram. [3 marks]
b) Graphically determine the direction of Trogdor's average acceleration
from t = 1 s to t = 7 s. Show the work involved in doing this. [2 marks]
c) When (between what times) is Trogdor speeding up? Explain how
you know. [2 marks]
S8. A roller coaster is going over the top of a loop. It is going quite fast and the loop is small so the riders notice
that they feel “pressed into their seats”.
a) Draw a free body diagram for a rider and another free body diagram for the roller coaster car. Indicate the
direction of the net force on both free body diagrams. [3 marks]
b) On your free body diagrams above, connect any forces that are members of action/reaction pairs. [1 mark]
Short answer total: /38
PHYS 1104 page 5 of 9 Dec. 9, 2011
Final Exam
Long Problems
Note that all quantities are given to 3 significant figures. Answers should be given to an appropriate
number of significant figures.
P1. A block of mass, M = 2.00 kg is attached to a string which hangs over a
pulley as shown. A force, Fpull = 8.00 N is exerted down on the end of the
string and it is found that the block remains stationary. The coefficient of
static friction between the block and the surface is 0.600 and the coefficient
of kinetic friction is 0.500.
a) What is the magnitude of the force of static friction acting on the block? Explain. [2 marks]
b) It is found that a force of 15.0 N is more than enough to make the block slide across the surface.
Find the acceleration of the block when this force is exerted on the string. [3 marks]
c) Now a counterweight, mc, with a weight of 15.0 N is hung on the end of the string as shown at
right. Will the acceleration of the block, M, be less than, the same as or greater than it was in part
b)? Explain. (Hint: If you are not sure then do the next part of the
problem and then come back to this part. However, be sure to interpret
your results from below to give an explanation. “The calculation says...”
is not a sufficient explanation.) [2 marks]
d) Draw free body diagrams for both masses. Then determine the acceleration of the block. [5
marks]
e) [BONUS] Interestingly, when there is friction, pulling horizontally does not result in the maximum
acceleration. Suppose we pull the block, M, with a tension force of 15 N angled at an angle of ? up.
What angle results in the maximum acceleration of the block? [4 marks]
page total: /12
+ /4 BONUS
PHYS 1104 page 6 of 9 Dec. 9, 2011
Final Exam
P2. Motors are limited more by power output than by the maximum force they can exert. That is,
they can exert large forces, as long as they do it at low speed. This can make it difficult to accelerate
something to high speed over a short distance using a motor. One solution to this problem is to use
a motor to compress a stiff spring and then release the spring to accelerate the object up to the
needed speed.
a) A machine needs to shoot nails into wooden toys that are being built on a production line. A motor
will compress a spring which will then be released to shoot the nail. The spring has a stiffness of 2.88
X 104
N/m. It is to be compressed 5.00 cm. The motor used to compress it has a power output of
50.0 W. How long does it take for the motor to compress the spring? [2 marks]
b) After the spring is compressed the nail is dropped in front of the spring and the spring is released.
The nail has a mass of 5.00 g. What is its speed as it exits the nail gun? [2 marks]
c) The nail embeds itself in a 500 g wooden toy which is initially at rest. How fast is the toy going
after the nail hits it? [2 marks]
d) To reduce the recoil of the toy it rests against a spring as
shown. The spring has a stiffness of 200 N/m and is
completely uncompressed when the nail hits the toy. The
friction coefficient between the toy and the surface is XXXXXXXXXXDraw an energy bar graph to describe
the energy transfers and transformations that occur during the recoil of the toy. [3 marks]
e) Find how far the toy recoils after the nail hits it. [3 marks]
page total: /12
PHYS 1104 page 7 of 9 Dec. 9, 2011
Final Exam
P3. The graph at right shows the position
vs. time graph for a 400 g mass hanging
on the end of a spring.
a) Write the position as a function of time
for this mass. [3 marks]
b) What is the spring constant of the spring? [2 marks]
c) What are the maximum speed and maximum magnitude of the acceleration of the mass? Indicate
on the graph when each of these occur. [3 marks]
d) What are the magnitude and direction of the spring force when the mass is at its maximum
height? [3 marks]
page total: /11
PHYS 1104 page 8 of 9 Dec. 9, 2011
Final Exam
P4. The graph at right shows the potential energy vs.
position for an object moving along the x-axis in some
region.
a) On the axes provided below the U vs. x graph, draw the
force vs. position graph for the object moving in this region,
complete with scales on the axes. [3 marks]
b) The object has a mass of 2.00 g and passes through x =
2.5 cm moving to the right with a kinetic energy of 2.00 J.
Will it ever reach x = 8 cm? Explain. [2 marks]
c) One the axes below, sketch (i.e. no scales on the axes are
needed) the position vs. time graph for this object. Show a
long enough time that the key features of the motion are
clear. [3 marks]
d) Is this an example of simple harmonic motion? Explain. [2 marks]
page total: /10
PHYS 1104 page 9 of 9 Dec. 9, 2011
Final Exam
P5. A blob of clay is stuck 20.0 cm from the center of a potter's wheel.
It's angular velocity vs. time graph is shown at right.
a) Sketch the angular acceleration vs time graph and the angular position
vs. time graphs on the axes provided. [4 marks]
b) What are the radial and tangential accelerations at t = 9.5 s? [4 marks]
c) The diagram below shows the potter's wheel, the direction of its
rotation and the blob of clay at t = 9.5 s. Approximately sketch the
acceleration vector at this instant onto the diagram. [2 marks]
d) How many rotations does the wheel go through between t = 0 and t =
8 s? [3 marks]
P6. After his last fiasco with the rocket and spring Wile E. is ready to try
again. This time everything goes perfectly and he reaches the end of the
slope going 60.0 m/s as planned. Now he is airborne. He has calculated
that the thrust of the rocket is enough to allow him to go over the top of
the cliff that is 120 m from the top of the slope. Unfortunately the rocket
malfunctions and stops providing thrust just as he leaves the top of the
slope, with predictable results.
a) What is Wile E.'s time of flight before slamming into the cliff? [3 marks]
b) How far up from the base of the cliff does Wile E. hit it? [3 marks]
page total: /19