PY105 Final Exam Makeup
December 20, 1999
Name:_______________________ Student Number:_________________
Signature:___________________________
Section:
[ ] A - Duffy [ ] B -Goldberg [
] C-Rothschild [
] D- Narain
The test is 120
minutes long. There are eight
questions, each worth 15 points, for a total of 120 points. Write your answers in the space
provided. If you need more space, write
on the back of the pages. Showing your work clearly will maximize your chances
of receiving partial credit. If
you do not show your work, you may not be given full credit, even if your
answer is correct. Remember to
state all answers with the appropriate number of significant digits, and with
appropriate units.
This is a closed-book test, but an equation sheet is
provided. Good luck!
For
staff use only: scores on each problem
Question 1 (/15): _____________
Question 2 (/15): _____________
Question 3 (/15): _____________
Question 4 (/15): _____________
Question 5 (/15): _____________
Question 6 (/15): _____________
Question 7 (/15): _____________
Question 8 (/15): _____________
Total (/120):
______________
[15 points] Problem
1. Pulleys
and Newton's Laws
1.
Two masses are attached together by a massless rope that runs over a massless
pulley as shown to the right. M1 = 10kgs and M2 = 15kg.
The coefficient of kinetic friction between M2 and the incline plane
is mk=
0.2.
a. [5 pts ] Draw the free body diagram for the
two masses.
b. [5 pts] Write down Newton's second law
equations for each of the masses.
c. [3 pts] Calculate the acceleration of the
mass M1.
11
11
[15
points] Problem 2. Springs,
slides and collisions
A
massless spring attached to a wall with spring constant K equal to 2.0 N/m is compressed a distance of 1 meter from its equilibrium position
by a mass m1 = 2.0
kg. After the spring is
released, m1 moves
across a frictionless, horizontal surface, slides down a frictionless slope, which drops a height h =0.5 m and then collides with a second
mass, m2 = 4.0 kg, which is at rest.
- [5 points] What is the speed of m1 just before it begins to go down the
slope.
- [5 points] What is the speed of m1 when it reaches the bottom of the
slope?
- [5 points] Assume that m1 sticks
to m2 when they collide, what is their speed after
the collision?
[15 points]
Problem. 3.
Rotational
dynamics
A)[ 6 points]
i)The
earth revolves around the sun in an elliptical orbit. As the earth moves closer
to the sun, the orbiting speed of the earth
[ ] does not change [
] increases [ ] decreases
[ ] it changes, but impossible to tell
which way
ii)As
a rocket moves further away from the
surface of the earth, the weight of the rocket
[ ] does not change [
] increases [ ] decreases
[ ] it changes, but impossible to tell
which way
iii) The moment of inertia of a solid cylinder
about its axis is given by 0.5 MR2.
If
this cylinder rolls without slipping, the ratio of it rotational kinetic energy
to its translational kinetic energy is
[ ] 1:1 [ ]1:2 [ ] 2:1 [ ]1:3
B) A
cylindrical shaped communications satellite of mass 1350 kg is set spinning at 2.21 rev/s about the
center axis and then launched from the shuttle cargo bay. The dimensions of the
satellite are : diameter = 1.56 m and length = 1.75 m. Calculate the
satellite’s
a) [
3 points] Rotational Inertia about the rotation axis:
b) [ 6 points ] Rotational kinetic energy
[15 points] Problem.
4. Static equilibrium - Walking
the plank
Problem 4 [15 points] – Walking the plank
(a) [8
points] If you have a mass of 50 kg, what maximum distance x beyond the roof
can you stand on the beam without tipping it over?
(b) [4
points] With you standing on the beam, what is the magnitude of the normal
force applied by the roof on the beam?
(c) [3
points] With you standing on the beam at x, the maximum distance point you
determined in part (a), where is the normal force applied by the roof on the
beam?
[ ] at the very edge of the roof [ ] at
the beam’s center-of-gravity
[
] evenly distributed over the 2.0 m of the beam in contact with the roof
[ ] 1.0 m to the left of the edge of the roof
[15 points]
Problem. 5.
Hydrodynamics
A fluid
flows through a pipe as shown in the diagram above. Assume the fluid is nonviscous and incompressible.
- [
5 points] If the velocity of the fluid is 10 m/s at point 2, which has a cross sectional area of
2.0 cm2 , what is the velocity of the fluid in
the pipe at point 1 where it is
wider with a cross sectional area 10
cm2.
- [5
points] If the difference in pressure between point 1 and 2 (P1
- P2).is 50,000 N/m2, what is the density of the
fluid?
- [5
points] A small tube which connects points 1 and 2, as shown in the
diagram, is partially filled with
a fluid. The fluid on the right
side of this small tube rises to a level h higher than on the
left side. Explain how you
would find the density of this fluid,
r,
using the information given in this problem (write an expression for r
as part of your answer).
[15 points] Problem
6. Simple Harmonic motion
A) [2 point] A mass at the end of a spring
oscillates both on the moon and the earth. It’s
period on the moon compared to that on earth
is
[ ] larger [ ]
smaller [ ] same
B) [
4 points] A mass is attached to a vertical spring which executes simple
harmonic motion between two points A and B. Where is the mass located
i) When it’s kinetic
energy is a maximum
[ ] At either A or B [ ] midway between A and B
[ ] quarter of the way between A and B,
measured from either A or B
[ ] None of the above
ii) When
the spring potential energy is a maximum
[ ] At either A or B [ ] midway between A and B
[ ] quarter of the way between A and B,
measured from either A or B
[ ] None of the above
C)
[2 point] A simple pendulum’s period is measured on the earth and the moon.
It’s
period
on the moon compared to that on the earth is
[ ] larger [ ]
smaller [ ] same
D)
[2 points] The pendulum of a grandfather’s clock is 1.5m long. It’s period on earth is
[ ]1.0s
[ ]1.5 s [
]2.0s [
]2.5s
E) In an electric shaver the blade moves back
and forth over a distance of 2.4mm. If this motion is described as a simple
harmonic motion with a frequency of 110 Hz, then find :
a) [2 points] Amplitude:
b) [3 points] The maximum acceleration of the
blade
[15 points]
Problem 7.
Calorimetry and thermal expansion
A) A
1.5kg mass of ice cubes at -25 oC is added to a 1.0kg mass of water
at +25 oC. The specific heat of ice is 2100 J/kg oC. The
specific heat of water is 4186 J/kgoC. The latent heat of fusion is 3.33
x105J/kg
a. [2 pts] How much heat is required to warm the
ice to 0 oC?
b. [2 pts] How much heat is lost in cooling the
water to 0 oC?
c. [3 pts] When the ice and water are allowed to
reach thermal equilibrium, what fraction is ice?
B) On the P vs. V diagram below,
a. [2 pts] Draw two isotherms, and label one hot
and one cold.
b. [2 pts] Choose a point A on the hotter isotherm and draw an isothermal expansion to a
point B. What is the relation
between the work done by the gas and the heat input during this part of the
cycle?
c. [2 pts] Draw and adiabatic expansion to the
colder isotherm, and describe the relationship between the internal energy of
the gas and the work done by the gas during this part of the cycle.
d. [2 pts] Complete the cycle with an isothermal
compression followed by an adiabatic compression back to the point A. Write down the expression for the
efficiency of this cycle in terms of the temperature of the hot and cold
isotherms.
[15 points] Problem 8.
Thermodynamics- A heat pump
A heat pump is a device that can extract heat from cold air and use
it to heat a house very efficiently. The P-V
graph for one cycle of a heat pump is shown.
Two
of the processes take place at constant volume, while the other two take place
at constant pressure.
(a) [3 points]
For a complete cycle of the heat pump, the work done by the system is …
[ ]
positive [ ] negative [ ] zero
Q = 360 J of heat is added to move the system
from state 1 to state 2 at constant pressure.
(b) [4
points] How much work is done by the
system in this process?
(c) [4
points] What is the temperature, T, of the system
in state 2?
(d) [4 points]
What is the volume, V, of the system
in state 2?