Q35 in TBR Physics Section II

[muhali3]

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Q35 in TBR Physics (Section II)

What is the net acceleration for the mass on the right side of the Atwood machine shown below?

A. a = (m1-m2)g / (m1 +m2)
B. a = (m1 + m2)g / (m1-m2)
C. a = g / (m1 + m2)
D. a = m2g / (m1 + m2)

The explanation says to use limiting cases to figure out the answer. It says that if you make m1 large and m2 small, it should give one value for acceleration. It says if you reverse the masses, and have m2 large and m1 small, then the magnitude of acceleration will be the same but the sign will be different. It says the only equation that passes that test is choice A.

But choice B passes that test too (if you plug in 1 and 0, for large/small respectively). I don't get why choice B is wrong.

 

[deleted393595]

Q35 in TBR Physics (Section II)

What is the net acceleration for the mass on the right side of the Atwood machine shown below?

A. a = (m1-m2)g / (m1 +m2)
B. a = (m1 + m2)g / (m1-m2)
C. a = g / (m1 + m2)
D. a = m2g / (m1 + m2)

The explanation says to use limiting cases to figure out the answer. It says that if you make m1 large and m2 small, it should give one value for acceleration. It says if you reverse the masses, and have m2 large and m1 small, then the magnitude of acceleration will be the same but the sign will be different. It says the only equation that passes that test is choice A.

But choice B passes that test too (if you plug in 1 and 0, for large/small respectively). I don't get why choice B is wrong.

The explanation is confusing because it doesn't really explain how to find the equation for acceleration. The key to the problem is that an Atwood machine is a simple pulley with masses connected by a rope on both sides. The heavier mass will fall down and pull the lighter mass up.

So, your equations are:

Fnet = Tension - mass2 * g = mass2 * a
Fnet = mass1 * g - Tension = mass1 * a

Tension should be same on both sides (Warning: Tension is not always same on both sides for a pulley if the pulley wheel rotates. PM me if you want to know more about this). Acceleration is also the same.

So isolate Tension in both equations and then set both derived equations equal to each other. Solve for acceleration and Bingo! You've got answer choice A.