Download PHYS 2053 SEC 0002 Fall 2008

EXAM #1 (70 min) PHYS 2053 SEC 0002
Name
Fall 2008
PID
THE EXAM CONSISTS OF A MULTIPLE CHOICE PART AND 4 PROBLEMS.
Your grade will be calculated as the sum of points in the multiple choice part plus
the highest 3 grades out of the 4 grades from the problems. ALWAYS SHOW
YOUR WORK or no credit.
MULTIPLE CHOICES (40 pts): Choose the one alternative that best completes the
statements or answers the question.
1. (5pts) Two equal masses of mass m are connected by a very light string over a
frictionless pulley of mass m/2. The system has been given a push to get it moving as
shown, but that push is no longer acting. In which segment of the string is the tension
greater?
A. The two tensions are the same
B. The tension in A is greater
C. The tension in B is greater
2. (5pts) A person pushes vertically downward with force P on a lever of length L that is
inclined at an angle θ above the horizontal as shown in the figure below. The torque that
the person’s push produces about a point A is:
A. PLcosθ
B. PLsinθ
C. PLtanθ
D. PL
3. (5pts) A uniform bar is hanging by a hook from the ceiling when it is suddenly struck
by a mass traveling horizontally. The mass sticks to the bar. Which quantities are
conserved during the collision?
A) Only angular momentum is conserved
B) Both angular momentum and linear momentum are conserved
C) Only kinetic energy is conserved
4. (5pts) . Two carts, one twice as heavy as the other, are at rest on a horizontal
frictionless track. A person pushes each cart with the same force for 7.00s. If the kinetic
energy of the lighter cart after the push is K, the kinetic energy of the heavier cart is:
A. 4K
B. 2K
C. K/2
D. K/4
E. K
5. (5pts) Two points are on a disk that rotates about an axis perpendicular to the plane of
the disk at its center. Point B is 3 times as far from the axis as point A. If the linear speed
of point B is V, then the linear speed of point A is:
A. 3V
B. V
C. V/9
D. 9V
E. V/3
6. (5pts) Two unequal masses m and 3m are attached to a thin bar of negligible mass that
rotates about an axis perpendicular to the bar. When m is a distance 3d from the axis and
3m is a distance d from the axis, the moment of inertia of this combination is I. If the
masses are now interchanged, the moment of inertia will be:
A. (7/3)I
B. (9/2)I
C. I
D. 9I
E. I/7
7. (5pts) Which of the following statements is true for an elastic collision?
A. Both momentum and kinetic energy are conserved.
B. Momentum is conserved, but kinetic energy is not conserved.
C. Kinetic energy is conserved, but momentum is not conserved.
8. (5pts) A heavy rifle initially at rest fires a light bullet. Which of the following
statements about these objects is true?
A. The bullet and rifle both gain the same magnitude of momentum.
B. The bullet and rifle both have the same acceleration during the firing.
C. The bullet and the rifle gain the same amount of kinetic energy.
9. (5pts) EXTRA CREDIT
In which of the following collisions would you expect the kinetic energy to be
conserved?
A. A bullet passes through a block of wood.
B. Two bull elk charge each other and lock horns.
C. Two asteroids collide by a glancing blow, but do not actually hit each other, their only
interaction being through gravity.
D. Two cars with spring-like bumpers collide at fairly low speeds.
Problem 1. (20pts)
+y
vA,f
A
B
α
450
vA,i = 3.5 m/s
mA = 2kg
+x
vB,i = -0.5 m/s
mB = 4kg
A stone A with mass mA = 2 kg was
thrown horizontally towards east
with a speed of 3.5 m/s. A second
stone with mass mB = 4kg was
thrown horizontally towards west
with speed of 0.5m/s. After collision,
stone A went north east with velocity
vA,f and stone B went south east, at
an angle of 45o below the x axis with
velocity vB,f of magnitude 0.25/ms.
vB,f = 0.25 m/s
1. (5pts) Calculate the initial total momentum of the system consisting of the two stones.
2. (5pts) Calculate the x component of the final velocity of stone A
3. (5pts) Calculate the y component of the final velocity of stone A
4. (5pts) Calculate the angle between the final velocity of stone A and the +x axis.
Problem 2 (20pts).
A distracted hummingbird with mass
mb = 1.8g was flying east with a speed
vb when it struck a piece of wood
(mass mw = 1kg) hanging from a tree.
At this moment, the bird got its beak
stuck in the wood and both the piece of
wood and bird start moving east with a
speed V = 0.3 m/s. Afterwards, the
piece of wood and the bird (together)
swing up to a maximum height h.
mb
mw
vb
h
V
1. (5pts) Calculate the height h.
2. (5pts) Calculate the initial velocity of the bird vb
3. (10pts) What would be the initial velocity of the bird if h = 5 cm (in this case, V is not
equal to 0.3 m/s)?
Problem 3. (20pts)
A bicycle racer is going downhill at 9.4 m/s when, to his horror, one of his wheels
comes off when he is 60.0 m above the foot of the hill. We can model the wheel as
consisting of a thin-walled cylinder 82.0 cm in diameter and a mass mc = 1.1 kg; and 8
spokes as slender rods with axis through the center of the wheel with mass ms = 0.1 kg for
each spoke.
1. (5pts) Calculate the moment of inertia of one of the 8 spokes, and the moment of
inertia of the thin-walled cylinder part of the wheel.
2. (5pts) Calculate the total moment of inertia of the wheel (consisting of a thin walled
cylinder and 8 spokes).
3. (5pts) Calculate the kinetic energy of the wheel just as it leaves the bike.
4. (5pts) How fast is the wheel moving when it reaches the foot of the hill if it rolled
without slipping all the way down?
Problem 4. (20pts)
Solid cylinder m = 3.5 kg
A solid cylinder of mass m = 3.5 kg and diameter
of 60 cm, rolls down without slipping along a
ramp. The ramp is inclined at an angle of 42o to
the horizontal. There is a frictional force in this
problem.
42o
1. (5pts) Calculate the moment of inertia of the cylinder
2. (5pts) Write the equations of motion for translational motion along the ramp and for
rotation about the axis through the center of mass of the cylinder.
3. (5pts) Calculate the acceleration of the cylinder acm.
4. (5pts) Calculate the friction force.