Exam
COLLEGE Final PHYSICS 101
December 3, 2007
NAME: ________________________________ Student ID #______________________
RECITATION SECTION and ROOM#: ______________________
Correct Room and
Correct Recitation Section Number
Problems
(10)
1)
2)
3)
4)
5)
6)
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(25)
(25)
(25)
(25)
(25)
(25)
Bonus
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(15)
TOTAL POINTS:
_______
(175)
IN COMPLETING THIS EXAM, YOU WILL NOT RECEIVE FULL CREDIT UNLESS YOU SHOW
AND EXPLAIN HOW YOUR ANSWERS WERE OBTAINED.
On problems with multiple parts, please attempt all parts. If you need an answer from a previous part
and do not have it, show how you would solve it as if you did have the answer.
| g | = 9.8 m/s2
v. 2
1.
The figure shows a uniform beam that extends beyond its support, like a diving board. Such a
beam is called a cantilever. The cantilever is in equilibrium. You identify the forces acting on the
beam as the weight of the beam (mg) located at the center of gravity, and the force on the beam due
to the two supports that you identify as FA and FB as shown above. You make the initial assumption
that FA and FB point upward; you call forces that point upwards positive.
(a) Write out the force and torque equations for equilibrium using your assumed force directions as
shown above. Choose an axis of rotation about point A, B or CG; clearly label which axis you are
using. (10 pts.)
(b) Is it necessary that FA be negative (ie. Point down instead of up)? (circle one) (5 pts.)
i) Yes, the net torque about A must be equal to the moment of inertia times the angular
acceleration.
ii) Yes, the net torque about B would otherwise not be zero.
iii) No, the net force must be equal to zero, but either FA or FB can be negative.
iv) No, FA is always positive.
(c) Find FB if the mass of the beam is 1800 kg. (10 pts.)
2. An eagle mA = 4.3 kg moving with speed vA = 7.8 m/s is on a collision course with a second eagle
mB = 5.6 kg moving at vB = 10.2 m/s in a direction perpendicular to the first. After they collide,
they hold onto one another.
(a) In what direction, and with what speed, are they moving after the collision? (15 pts.)
(b) Calculate how much energy was lost in the collision? (10 pts.)
3. A teenager pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it
from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of
diameter 2.5 m and has a mass of 160 kg, and two children (each with a mass of 25 kg) sit opposite
each other on the edge. Neglect the mass of the teenager who is pushing the merry-go-round.
(a) Calculate the moment of inertia of the plus merry-go-round children. (6 pts.)
(b) Calculate the torque required to produce the acceleration, neglecting any frictional torque. (6 pts.)
(c) What force is required at the edge to produce this torque? (6 pts.)
(d) Calculate the angular displacement of the merry-go-round in the 10s the torque was applied? (7 pts.)
4. Parts A. and B are separate problems.
A. According to a simplified model of a mammalian heart, at each pulse approximately 20 g of blood is
accelerated from 0.25 m/s to 0.35 m/s during a time of 0.10 s. What is the magnitude of the force
exerted by the heart muscle on the blood? (10 pts.)
B. A 65-kg ice skater coasts with no effort for 75 m until she stops. The coefficient of kinetic friction
between her skates and the ice is K = 0.10
(a) Draw a free body diagram of the skater clearly showing all the forces that act on her. (5 pts.)
(b) Determine how fast was she moving at the start of her coast? (10 pts.)
5. A ball is tossed from an upper-story window of a building. The ball is given an initial
velocity of 8.00 m/s at an angle of 20.0 below the horizontal. It strikes the ground 3.00 s later.
(a) How far horizontally from the base of the building does the ball strike the ground? (8 pts.)
(b) Determine the height from which the ball was thrown. (8 pts.)
(c) How fast is the ball traveling just before it hits the ground? (9 pts.)
6.
A 65-kg student runs at 5.0 m/s grabs a rope, and swings out over a lake, see figure below. He
releases the rope when his velocity is zero. The distance from where the rope is attached to the tree
limb to the students center of mass is 10.0 m, as shown below.
(a) Calculate how high the student is above his starting point,
when he releases the rope, as shown in the figure.? (6 pts.)
b) Through what angle does he swing? (6 pts.)
(c) What is the tension in the rope just before he releases it, ei. when his velocity is zero? Draw a free
body diagram of the student showing the forces acting on him. (6 pts.)
(d) What is the maximum tension in the rope? (Hint: the maximum tension occurs just when the running
student grabs the rope and the rope supports his weight. The answer is not mg) (7 pts.)
Bonus Question:
A figure skater spins at a rate of 0.86 rev/s. If she pulls her arms and free leg in close to the spin axis, the
speed of rotation increases to 2.5 rev/s.
(a) By what factor (Ifinal / Iinitial) has her moment of inertia changed? (5 pts.)
(b) By what factor (KEfinal / KEinitial) has her rotational kinetic energy changed? (5 pts.)
(c) Explain how the kinetic energy of the skater can change without violating energy conservation. (5
pts.)