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Laws of Motion: Atwood,s Machine, spacial cases

I have no clue how to go about getting these equations. Can you help me out and explain how to do these. It is not for a test or anything. It is just a homework problem, but I can't figure it out.

(See attached file for full problem description and equations)

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Atwood Machine Special Cases:
An Atwood machine consists of two blocks (of masses and ) tied together with a massless rope that passes over a fixed, perfect (massless and frictionless) pulley. In this problem you'll investigate some special cases where physical variables describing the Atwood machine take on limiting values. Often, examining special cases will simplify a problem, so that the solution may be found from inspection or from the results of a problem you've already seen.

For all parts of this problem, take upward to be the positive direction and take the gravitational constant, , to be positive.

a.) Now, consider the special case where the block of mass is not present. Find the magnitude, , of the tension in the rope. Try to do this without equations; instead, think about the physical consequences.
Answer: T=?

b.) For the same special case (the block of mass not present), what is the acceleration of the block of mass ?
Express your answer in terms of , and remember that an upward acceleration should be positive.
Answer: a2=?

c.) Next, consider the special case where only the block of mass is present. Find the magnitude, , of the tension in the rope.
Answer: T=?

d.) For the same special case (the block of mass not present) what is the acceleration of the end of the rope where the block of mass would have been attached?
Express your answer in terms of , and remember that an upward acceleration should be positive.
Answer: a2=?

e.) Next, consider the special case . What is the magnitude of the tension in the rope connecting the two blocks?
Use the variable in your answer instead of or .
Answer: T=?

f.) For the same special case ( ), what is the acceleration of the block of mass ?
Answer: a2=?

g.) Finally, suppose , while remains finite. What value does the the magnitude of the tension approach?
Answer: T=?
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Solution Summary

7 parts of the problem related to Atwood Machine are solved and explained.

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