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Faculty of Engineering and Department of Physics
Engineering Physics 131
Final Examination
Saturday April 18, 2009; 2:00 pm – 4:30 pm
1. No notes or textbooks allowed.
2. Formula sheets are included (may be removed).
3. The exam has 9 problems and is out of 50 points. Attempt all parts of all problems.
4. Show all work in a neat and logical manner.
5. Write your solution directly on the pages with the questions. Indicate clearly if you use the
backs of pages for material to be marked.
6. Non-programmable calculator allowed. Turn off all cell-phones, laptops, etc.
DO NOT separate the pages of the exam containing the problems.
NAME:
______________________________________
ID#:
___________________
Please circle the name of your instructor:
B01: Chow
B02: Kaminsky
B03: Swain
B04: Raboud
B05: Ropchan
B06: Tang
Please do not write in the table below.
Question
Value (Points)
1
4
2
3
3
2
4
3
5
9
6
8
7
7
8
8
9
6
TOTAL
50
Mark
1. [4 Points]
The net force acting on a 3.00-kg particle undergoing rectilinear motion is shown in the graph below. If its
speed is v = 3.00 m/s when x = 0, determine the following:
a) The maximum acceleration of the particle;
b) Its maximum speed;
c) The total work done on the particle by the force as it moves from x = 0 m to x = 10 m.
2. [3 points]
A particle of mass m is constrained to move along a circular track (of unit radius) in a horizontal plane.
When the particle is at the position shown it is moving counterclockwise around the track with a speed ν0
when a constant force P is applied to the particle. This same force P is applied during the rest of the time
that the particle is moving. The particle's position-dependent speed as it moves around the circle in three
separate cases is shown in the graphs below.
For each of the three cases below, draw the direction of the force P applied to the particle.
3. [2 Points]
A system which consists of two masses A and B connected by a single cable wrapped around several
pulleys is shown below. As shown in the diagram below, mass A sits on a smooth surface and is
connected to a fixed surface by a spring with spring stiffness k. Suppose the system is released from rest
and mass B descends a distance h (> 0) from its initial position.
(I) Assume the spring is initially unstretched.
If the pulleys are massless, Block A will attain a speed v1 after Block B has descended a distance h. If the
pulleys have finite mass, Block A will attain a speed v2 after Block B has descended a distance h. Which
of the following is true?
(a)
(b)
(c)
(d)
v1 is greater than v2
v1 is less than v2
v1 is the same as v2
Insufficient information to tell.
Answer: _______________
(II) Assume that the pulleys are massless.
If the spring in the diagram is initially not stretched, Block A will attain a speed v1 after Block B has
descended a distance h. If the spring in the diagram is initially stretched, Block A will attain a speed v2
after Block B has descended a distance h. Which of the following is true?
(a)
(b)
(c)
(d)
v1 is greater than v2
v1 is less than v2
v1 is the same as v2
Insufficient information to tell.
Answer: _______________
4. [3 Points]
The figures below show four identical compound pulleys, each composed of two uniform cylinders (of
different radii) attached so that they rotate without friction as a unit about their common center. Ropes are
wound about each cylinder and the end of each rope is either attached to a block of mass m, or pulled
downwards. In the figure below, each square denotes a block of mass m and each arrow represents an
applied force of magnitude mg.
Rank the four scenarios according to the angular acceleration of the compound pulley, from greatest to
least. Indicate any ties.
Answer: _______________________
mg
(A)
(B)
mg
(C)
mg
mg
(D)
5. [9 Points]
A 1.00 kg block is at rest at the top of a smooth hemispherical surface of radius 2.00 m. It is attached to
an unstretched elastic cord with spring stiffness of 5.00 N/m as shown on the left diagram below. The
block is given a slight push to the right, causing it to slide down the surface. When the block has moved to
the position shown on the right diagram below:
a) Show that cord has been stretched by 0.6357 meters (compared to the unstretched length).
b) What is the speed of the block?
c) What is the magnitude of the normal force acting between the block by the surface?
d) What is the magnitude of the tangential acceleration?
unstretched
elastic cord
smooth
surface
R
R
R
60°
6. [8 Points]
A sliding box encounters a rough surface inclined at 10.0 degrees below the horizontal. At point P, i.e. the
start of the incline, the speed of the box is 4.50 m/s. The coefficient of kinetic friction μk varies on the
incline as follows: μk= 0.200 at point P, varies linearly with distance from point P, and reaches a value of
μk= 0.700 a distance x = 12.5 m from P. Beyond x =12.5 m, μk= 0.700 and is constant.
a) Determine a formula for μk(x), where x denotes the distance (in meters) traveled from point P.
b) Determine the total distance the box travels along the incline before coming to rest.
7. [7 Points]
A 10.0 kg package drops from a chute into a 25.0 kg cart which is initially at rest and sitting on a flat
surface. Just before the package hits the cart, the package has a velocity of 3.00 m/s at an angle of 30.0
degrees below the horizontal. The package and cart then move together. Determine
(a) the final velocity (magnitude/direction) of the cart,
(b) the impulse (magnitude/direction) exerted by the cart on the package.
8. [8 Points]
The ball hits the wall at Point A with a (horizontal) velocity v0 of magnitude 8.00 m/s to the right (see
diagram). Note that Point P is 1.00 m above the ground. The coefficient of restitution between the ball and
the wall is 0.900. The ball then bounces from the wall and hits the ground at point B, as indicated by the
dashed line in the diagram below. Neglecting friction, determine the horizontal distance d from the foot of
the wall to the point B where the ball will hit the ground after bouncing off the wall.
9. [6 Points]
A solid spherical ball of mass m and radius R rolls without slipping up an incline that makes an angle θ
with the horizontal. Note: Moment of inertia of the sold spherical ball is I = (2 / 5)mR 2 .
x
ω0
v0
θ
If the initial angular speed of the ball at the bottom of the incline is ω0,
a) What is its angular speed after it has rolled a distance of x along the incline?
b) What is the magnitude and direction of the friction force acting on the ball?
(All answers should be only expressed in the following symbols: m, θ, ω0, g, x and R.)
Extra Page (for rough work, etc.)