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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In a simulation, m1 is 1.0 kg and m2 is 1.1 kg. Mass m2 rests on the floor that exerts a normal force, FN, on m2. There is no motion (i.e.. the system is in equilibrium). What is the normal force, FN, and what is the tension, T, in the rope? T (at t = 2.54 s) = ______. At equilibrium: FN + T - m2 ? g = 0. Then FN = _______.

An Atwood machine has a mass of 3.50 kg connected by a light string to a mass of 6.00 kg over a pulley with a moment of inertia of 0.0352 kg and a radius of 12.5 cm. If the system is released from rest, what is the speed of the masses after they have moved through 1.25 m?
2.00 m/s
2.28 m/s
4.00 m/s
4.95

Physicists say that it is impossible to create a perpetual motion machine, a machine whose own activity keeps it running perpetually. What energy principle precludes the possibility of a perpetual motion machine?

An Atwood machine consists of masses of 1.5 kg and 1.66 kg on opposite sides of a light frictionless pulley. The system is given an initial velocity of 1.15 m/s in the direction of the 1.5 kg mass.
* How much work does gravity do on the system between the initial instant and the instant at which the system comes to rest, and

Please help with the following problem. Provide step by step calculations.
An Atwood machine consists of masses of 1.9 Kg and 1.995 Kg hanging from opposite sides of a pulley.
As the system accelerates 3.3 meters from rest, how much work is done by gravity on the system?
Assuming no friction or other dissipative forces

Two hypothetical planets orbit their star according to Kepler's laws of planetary motion.
If one of the planets has an orbit which has a semimajor axis three time that of the other, then numerically how much greater is it orbital period compared to the other?

The first question involves an atwood machine, the second involves two different rods attached to hinges falling/rotating to the ground.
See the jpeg for exact questions. The text is provided below simply for the benefit of the search engine:
Atwood Machine
A frictionless pulley with mass Mb is attached to the ceiling,

(Please see the attached file for detailed problem and fig.)
The two blocks, m1 = 3.0 kg and m2 = 4.9 kg, in the figure (see attachment) are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0