PHYSICS 115 - FINAL EXAMINATION PAGE 13 OF 13
UNIVERSITY OF WATERLOO
DEPARTMENT OF PHYSICS
Physics 115 - Mechanics
Final Examination
December 8, 2006 9:00– 11:30 Time: 2.5 Hours
Name: (Print) Division
ID # Signature
Professor: Circle One
R. Jayasundera [Mec. St. 4]008 D. Strickland [Elec. St. 4]005 F. Mansour [Chem]001
R. Jayasundera [Mec. St. 8]007 D. Strickland [Elec. St. 8]006 F. Mansour [Env.Chem] 002
R. Allahverdi [Comp.]004 M. Fich [Civil] 003 M. Balogh [Softw.]009
Aids Permitted: Calculator, attached formula sheet
ATTEMPT ALL QUESTIONS
Important Instructions - Read Carefully
1. Part A has 20 questions, worth 20%.
2. Part B has 6 questions, worth 80%; 1 question per page; recommended average time per question: approximately 20 minutes
3. Check that your booklet has 13 pages (including 1 blank sheet at the back and this cover plus a formula sheet). Questions are to be answered on this paper. Use the space under each question first. If necessary continue on back of previous sheet and then on the blank sheet, and indicate by writing “continued at left” or “continued on page 11”. Answers must include units where appropriate.
4. In Part A, the letter corresponding to each answer must be entered on your computer sheet in dark lead PENCIL only. Avoid erasures by checking answers before marking them. Mark your I.D. Number and Division Number in the space provided. Also (THIS IS IMPORTANT) fill in the correct ovals for your I.D. Number and Division. Do not mark “card number” column. Check that you have not missed, or put double marks in any row in the answer field.
5. Print name, etc., in the upper right part of your computer sheet and at the top of this page.
6. There is no penalty for marking incorrect answers.
7. **NOTE: KEEP COMPUTER SHEET FACE DOWN WHEN NOT IN USE **
8. **NOTE: COMPUTER SHEETS WILL BE COLLECTED AFTER 2 HOURS
9. In Part B, answers must be entered in the boxes provided. These will be hand-marked, and part marks will be given liberally, if your solutions clearly show correct thinking.
10. Ask a proctor to clarify a question if you think that is necessary.
GOOD LUCK !
Use g = 9.80 m/s2
(NOTE: Assume all given data is accurate to three significant figures if needed)
Moment of Inertia (about axes through centre of mass).
Cylinder or Disk (mass M, radius R, axis ^ to radius) : ICM = (1/2) MR2. Solid Sphere (mass M, Radius R) : ICM = (2/5) MR2 Hoop (mass M, radius R, axis ^ to radius): ICM = MR2 Rod (mass M, length L, axis ^ to length) ICM = (1/12) ML2.
MARKSONLY / 1B / 2B / 3B / 4B / 5B / 6B / TOTAL
Computer Sheets Collected After 2 Hours
PHYSICS 115 - FINAL EXAMINATION PAGE 13 OF 13
1. Vector lies in the xy plane. For what orientation of vector will its components
have opposite signs.
(a) 1st quadrant
(b) 1st and 2nd quadrant
(c) 2nd and 4th quadrants
(d) 1st and 4th quadrants
(e) 2nd and 3rd quadrants
2. A baseball is thrown with an initial speed of . When it reaches the top of
its trajectory the velocity and acceleration are
(a)
(b)
(c)
(d)
(e)
3. A crate is sitting in the center of a flatbed truck. If the crate does not slide on the truck,
while the truck is accelerating to the right, the direction of the frictional force acting on
the crate is pointing to the
(a) right
(b) left
(c) no frictional force since the crate is not sliding
(d) all of the above
(e) none of the above
4. The observer in the elevator which is accelerating upward at “a” m/s2, would claim that
the weight of the fish is the
(a) reading of the scale
(b) reading of the scale + ma
(c) reading of the scale – ma
(d) reading of the scale times a
(e) none of the above
(m is the mass of the fish)
5. As a simple pendulum swings back and forth, the forces acting on the suspended masses
are (i) force of gravity (ii) the tension of the cord and (iii) air resistance.
The work done by each of the above forces can be written as Wg, WT, Wair = Wa (note Wg =
work done by gravity etc). Which statement is always true?
(a) Wg > 0. Wa < 0
(b) Wg < 0. WT = 0
(c) Wa = 0, WT = 0
(d) Wa < 0, WT = 0
(e) WT > 0, Wa = 0
6. Two objects are at rest on a frictionless surface. Object 1 has a greater mass than object
2. When a force “F” is applied to object 1, it accelerates through a distance “d”. The
force “F”, is removed from object 1 and applied to object 2. At the moment when object
2 has accelerated through the same distance d, which of the statements is true.
(a) P1 > P2
(b) K2 > K1
(c) K1 = K2
(d) P1 = P2
(e) none of the above
7. A small sports car collides head-on with a massive truck.
Which vehicle experiences the greater magnitude force during the collision?
(a) The car
(b) The truck
(c) The answer depends on the speeds the vehicles were moving
(d) Both experience the same force during the collision
8. Two marbles, one with twice the mass of the other, are dropped to the ground from a
table. Just before hitting the ground, the more massive marble has:
(a) As much kinetic energy as the lighter one.
(b) Twice as much kinetic energy as the lighter one.
(c) Half as much kinetic energy as the lighter one.
(d) Four times as much kinetic energy as the lighter one.
(e) Impossible to determine.
9. Three framed pictures of identical shape and mass m were hanged as shown below.
Which way of hanging the picture requires a stronger string?
(a) 1
(b) 2
(c) 3
(d) 1 and 2 (both are the same)
(e) all are the same
10. A wheel starts from rest and spins with a constant angular acceleration. As time goes on
the acceleration vector for a point on the rim:
(a) decreases in magnitude and becomes more nearly tangent to the rim
(b) decreases in magnitude and becomes more nearly radial
(c) increases in magnitude and becomes more nearly tangent to the rim
(d) increases in magnitude and becomes more nearly radial
(e) increases in magnitude but retains the same angle with the tangent to the rim
11. A ball is rolling freely on a flat surface.
(a) The force of friction points opposite to the motion of the centre of mass.
(b) The force of friction points in the direction of motion of the centre of mass.
(c) The force of friction cannot be determined.
(d) The force of friction is zero.
(e) None of the above.
12. You are holding onto a spring that is already stretched. You then proceed to take that
spring to equilibrium slowly.
(a) The work you do is positive.
(b) The change in potential energy of the spring is positive.
(c) Your work is double that of the work of the spring.
(d) The spring does negative work.
(e) The spring does positive work.
13. You throw a tennis ball of radius R on the floor such that it rolls freely on a flat surface
for some time and then it hits a patch of ice where the coefficient of friction between the
ball and the ice is s = 0. When the ball hits the patch
(a) It continues to roll as before.
(b) It starts to spin
(c) It begins to skid
(d) none of the above
14. A car is driving at a constant speed on the 401 heading towards Montreal. The driver hits
the gas pedal and the engine delivers more power. During the time when the driver is
pressing on the gas pedal (the wheels are always rolling)
(a) The force of friction points opposite to the motion.
(b) The force of friction does not play a role because the speed of the bottom of the wheel is
zero
(c) The force of friction is zero because the wheel is always rolling.
(d) The force of the friction points in the same direction as the velocity of the center of mass.
(e) None of the above
15. An elevator is going up at a constant speed, pulled by a single cable. How does the
tension (T) in the cable compare with the weight of the elevator (W)?
(a) T > W
(b) T = W
(c) T < W
(d) impossible to tell
16. The angular velocity vector of a spinning body points out of the page. If the angular
acceleration vector points into the page then:
(a) the body is slowing down
(b) the body is speeding up
(c) the body is starting to turn in the opposite direction
(d) the axis of rotation is changing orientation
(e) none of the above
17. Which object has the largest moment of inertia? (masses are point masses connected to
massless rods)
18. In which of the following diagrams of a door hinged to a wall at two points A and B at ¼
and ¾ of the length if the door, show the forces in the directions that would result in the
door being in static equilibrium.
19. Which pulley will be spinning fastest when the block hits the ground, if all start from
rest? Assume the strings do not slip and pulleys are discs.
20. The figure shows four disks that are on a frictionless floor. Three forces, of magnitude F,
2F, or 3F, act on each disk, either at the rim, at the center, or halfway between the rim and the center as shown in diagrams. Which disk is in equilibrium?
(a) (b) (c) (d)
1B. A toy gun fires marbles with a velocity v = 7m/s.
(a) To hit a toy soldier that is 1.8 m away and 1.1 m higher than the gun, at what angle
should the gun be aimed?
(b) Now assume that the toy soldier is dropped (starting from rest) the instant the gun is
fired. If the gun is aimed at the toy soldier when it is fired, at what height above the
ground will the soldier be when it is hit by the bullet?
(c) How long after firing does the bullet hit the soldier?
2B. The 20 kg mass is free to slide down an incline of 45º. The
pulley is massless and the 20 kg mass is connected to a 5 kg
mass as shown. Initially the string connecting the 20 kg mass
to the other is vertical. If the system is released from rest.
(a) Find the speed of the 5 kg mass when 20 kg mass has moved to
position “B” as shown in diagram if the incline was smooth. A
(b) If the plane was rough and k = 0.21 what is the acceleration of the 20 kg mass
when it is at point A (assume k = 0.21 for part c and d).
(c) Find the acceleration of the 20 kg mass at the position B, if the pulley was heavy and has
a moment of inertia about the center of mass (axis of rotation) of .25 kg m2.
(d) Find the tensions of the string at position B.
3B. A uniform wooden sign of mass 4.0 kg hangs beside a building wall. The sign is 2.00 m
high and 4.00 m wide. It is supported by a hinge at P, that is midway up one
edge, and by a light rope that is attached exactly three-quarters of the distance across the
upper edge. The rope makes an angle of 20.0 degrees with the horizontal.
(a) Complete the free body diagram by showing all the forces acting on the sign; show
where on the sign each of the forces acts.
(b) Write the conditions for static equilibrium of the sign and solve for the horizontal (H) and
vertical (V) components of the force at P, and solve for the rope tension (T)
Later, Prof. Fich of mass 90.0 kg climbs out of a window just below the sign, reaches up
and grabs onto the bottom portion of the sign and, while hanging from the sign, begins to move away from the building. If the rope can only support a maximum tension of 1500 N, how far can Prof. Fich move away from the building ?
4B. A uniform rod of mass m and length is pivoted at one end is free to rotate in a
vertical plane. There are 2 disks each of mass m and radius r attached to the rod
as shown in the diagram. A rubber bullet of mass mb is shot at the rod and it
sticks to the rod at a distance h from the pivot. If the speed of the bullet just before
it collides with the rod is 50 m/s, m = 2 kg, = 1m, r = 20 cm, mb = 0.5 kg
and h = 80 cm.
(a) Find the linear momentum of the bullet just before impact.
(b) Find the angular momentum of the system just before impact.
(c) Find the moment of inertia of the system after the bullet has collided.