Download Assignment #11 Due by 10 pm November 24, 2009

PHYSICS 105
Assignment #11
Due by 10 pm November 24, 2009
NAME: __________________________________________
DISCUSSION SECTION: [ ] D7 – W 9 am
[ ] D9 – W 11 am
[ ] F 1 – W 1 pm
[ ] F4 – W 4 pm
[ ] D3 – F 11 am
[ ] D8 – W 10 am
[ ] F2 – W 2 pm
[ ] F5 – W 7 pm
[ ] HS – W 10 am
[ ] F3 – W 3 pm
[ ] D1 – F 9 am
[ ] D4 – F 12 pm [ ] D5 – F 1 pm (Asma)
[ ] D2 – F 10 am
[ ] D6 – F 1 pm (John)
PLEASE CHECK OFF YOUR DISCUSSION SECTION ABOVE!
INSTRUCTIONS:
1. Please include appropriate units with all numerical answers.
2. Please show all steps in your solutions! If you need more space for calculations, use the
back of the page preceding the question. For example, calculations for problem 3 should be
done on the back of the page containing question 2. You must show correct work to
receive full credit. Support your answers with brief written explanations and/or arguments
based on equations.
3. Indicate clearly which part of your solution is the final answer.
4. Try answering these problems, as much as possible, without a calculator and using only
the equation sheet to help you. This will help you prepare for the test.
5. Grading scheme for each problem: each part of each problem is worth 2 points. You
get 0 if your answer is wrong or mostly wrong, 2 if your answer is correct, and 1 if your
answer is mostly correct.
Please do your draft work of the assignment elsewhere, and copy your
work over neatly when you hand in the assignment. The graders will
deduct points for work that is difficult to follow.
Angle (θ)
sin(θ)
cos(θ)
30˚
1
2
3
2
2
2
1
2
45˚
60˚
2
2
3
2
Problem 1: ____
tan 
sin 
cos
Problem 2: ____
Problem 3: ____
Problem 4: ____

Problem 5: ____
TOTAL:
_____
PROBLEM 1 – 10 points
A uniform solid sphere with a mass of M = 1.6 kg and radius R = 20 cm is rolling without
slipping on a horizontal surface at a constant speed of 3.0 m/s. It then encounters a ramp inclined
at an angle of 10˚ with the horizontal, and proceeds to roll without slipping up the ramp. The
goal of this problem is to determine the distance the sphere rolls up the ramp (measured along
the ramp) before it turns around, and to use conservation of energy to do so.
[2 points] (a) Sketch this situation, showing the sphere in two positions, one at the bottom of the
ramp and the other when the sphere reaches its highest point.
[2 points] (b) Start with the usual conservation of energy equation: K i  U i  Wnc  K f  U f .
Identify all the terms that are zero in this equation, and explain why they are zero.
[2 points] (c) Write out expressions for the remaining terms. Remember to account for both
translational kinetic energy and rotational kinetic energy, if appropriate. Keep everything in
terms of variables.
[2 points] (d) How far does the sphere roll up the ramp (measured along the ramp)? First find an
expression for this distance in terms of variables, simplified as much as possible, and then plug
in the appropriate values.
[2 points] (e) How far would the sphere have traveled up the ramp if the ramp were frictionless?
PROBLEM 2 – 10 points
Case 1 and case 2 show two situations of a block
hanging from a string wrapped around the outside of
a pulley. The blocks are identical, and the pulleys
are uniform solid disks of the same radius, but the
pulley in case 2 has twice the mass (and therefore
twice the moment of inertia) of the pulley in case 1.
The systems are released from rest at the same time,
and in both cases the block accelerates down.
Friction can be neglected.
[2 points] (a) In which case is the acceleration of the block larger?
[ ] case 1
[ ] case 2
[ ] equal in both cases
[2 points] (b) In which case is the tension in the string, while the block is falling, larger?
[ ] case 1
[ ] case 2
[ ] equal in both cases
[2 points] (c) In which case is the net torque on the pulley, while the block is falling, larger?
[ ] case 1
[ ] case 2
[ ] equal in both cases
[2 points] (d) In which case does the block have a higher speed as it approaches the ground?
[ ] case 1
[ ] case 2
[ ] equal in both cases
[2 points] (e) In which case does the pulley have a larger rotational kinetic energy, measuring the
kinetic energy just before the block reaches the ground in each case?
[ ] case 1
[ ] case 2
[ ] equal in both cases
PROBLEM 3 – 8 points
Consider the three cases
shown. Each case involves a
ball of mass 2m interacting
with either one or two other
balls. In each case, account
only for the gravitational force
exerted by the balls on one another. Each ball is a distance d from the origin, except for the ball
of mass m in case B, which is at the origin.
[2 points] (a) Rank the cases based on the magnitude of the net force exerted on the ball of mass
2m.
[ ]A>B>C
[ ]C>A>B
[ ]A=B>C
[ ]C>B>A
[ ]B>A>C
[ ]B>C>A
[ ]C>A=B
[2 points] (b) Calculate the magnitude of the net force exerted on the ball of mass 2m in case A.
[2 points] (c) Comparing case B and case C, in which case is the gravitational potential energy of
the system more negative (i.e., has the smallest actual value)?
[ ] case B
[ ] case C
[ ] neither, they’re equal
[2 points] (d) Calculate the gravitational potential energy of the system in case A.
PROBLEM 4 – 10 points
You have two identical springs and two identical blocks. You attach each block to a spring so
you have two spring-block systems, and you set the blocks up to oscillate simultaneously on a
frictionless horizontal surface. You pull the blocks so they stretch their respective springs,
releasing them both from rest simultaneously. However, when you release the blocks one of
them (we’ll call this system 1) is displaced a distance A from equilibrium and the other (we’ll
call this system 2) is displaced 2A from equilibrium.
[2 points] (a) If the block in system 1 reaches a maximum speed v in its oscillations, what is the
maximum speed reached by the block in system 2?
[ ]
v
2
[ ]v
[ ]
[ ] 2v
2v
[ ] 4v
[2 points] (b) If the block in system 1 experiences oscillations with a period T , what is the period
of the oscillations experienced by the block in system 2?
[ ]
T
2
[ ]T
[ ]
[ ] 2T
2T
[ ] 4T
[2 points] (c) If the maximum force experienced by the block in system 1 is Fmax , what is the
maximum force experienced by the block in system 2?
[ ]
Fmax
2
[ ] Fmax
[ ]
2 Fmax
[ ] 2 Fmax
[ ] 4 Fmax
[2 points] (d) If the potential energy stored in the spring in system 1 is U i when the block is first
released from rest, what is the potential energy initially stored in the spring in system 2?
[ ]
Ui
2
[ ] Ui
[ ]
2 Ui
[ ] 2U i
[ ] 4U i
[2 points] (e) At a particular instant, some time after being released, the block in system 1 is
20 cm from its equilibrium position. How far from equilibrium is the block in system 2 at that
same instant?
[ ] 10 cm
[ ] 20 cm
[ ] 40 cm
[ ] there is not enough information to answer this question
PROBLEM 5 – 10 points
A block on a horizontal
frictionless surface is
attached to a spring. The
spring is at its natural
length when the block is at
x = 0. At time t = 0, the
block is released from rest
at the point x = A. Graph 1
represents the position of
the block as a function of
time for one complete
oscillation.
Considering one complete oscillation …
(a) Which graph shows the block’s velocity as a function of time? _________
(b) Which graph shows the block’s acceleration as a function of time? ________
(c) Which graph shows the block’s kinetic energy as a function of time? ________
(d) Which graph shows the block’s potential energy as a function of position? _______
(e) Which graph shows the magnitude of the net force acting
on the block as a function of position?
_______
In a second experiment, instead of being released from rest, the block is given a push, so at t = 0
it starts moving from the origin to the right with speed v. Graph 3 represents the position of the
block as a function of time for one complete oscillation. Considering one complete oscillation …
(f) Which graph shows the block’s velocity as a function of time? _________
(g) Which graph shows the block’s acceleration as a function of time? ________
(h) Which graph shows the block’s kinetic energy as a function of time? ________
(i) Which graph shows the block’s potential energy as a function of position? _______
(j) Which graph shows the magnitude of the net force acting on
the block as a function of position? (Neglect the initial push.)
_______