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Class PH1110A2007
Assignment 15
Due at 5:00pm on Friday, October 5, 2007
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Weight and Wheel
Consider a bicycle wheel that initially is not rotating. A block of mass
is attached to the wheel and is allowed to fall
a distance
. Assume that the wheel has a moment of inertia
about its rotation axis.
Part A
Consider the case that the string tied to the block is attached to the outside of the wheel, at a radius
. Find
, the angular speed of the wheel after the block has fallen a distance
, for
this case.
Hint A.1 How to approach this problem
The most straighforward way to solve this problem is to use conservation of mechanical energy. The total initial
energy of the system is equal to the total final energy of the system (where the system consists of the wheel and the
block). In other words,
.
Where
is the initial energy of the system,
is the final energy of the block and
is the final energy of the
wheel.
Part A.2 Initial energy of the system
Initially, the wheel is not rotating. The initial energy of the system consists of the gravitational potential energy
stored in the block, since it is not moving either. Supposing that the gravitiational potential energy of the block is
zero at "ground level," find the initial energy of the system.
ANSWER:
=
What about the potential energy for the wheel? If you were to be very particular, you would either need to assign
some potential energy for the wheel, or choose a different reference height for it (located at it's center), such that
it's potential energy was zero. However, since you know that the (center of mass of the) wheel does not move, it's
potential energy does not change and as such you don't really need to calculate it. Again, this is because it is the
changes
is potential energy and not the absolute value of potential energy that are important.
Part A.3 Final energy of block
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Find the final energy of the block.
Part A.3.a Final velocity of the block
Find
, the magnitude of the final velocity of the block.
Express the velocity in terms of
and the final angular velocity of the wheel,
.
ANSWER:
=
Express the final energy of the block in terms of given quantities (excluding
) and the
unknown final angular velocity of the wheel,
.
ANSWER:
=
Since we are measuring potentials w.r.t. the ground for the block, the final potential energy of the block is zero.
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This note was uploaded on 04/29/2008 for the course PH 1110 taught by Professor Kiel during the Fall '08 term at WPI.
 Fall '08
 Kiel
 Mass

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