Each figure below shows an Atwood machine with two blocks hanging from the ends

Question

Each figure below shows an Atwood machine with two blocks hanging from the ends of a strong but massless string that passes over a frictionless pulley. In each figure, the block on the left is more massive than the one on the right, so the block on the left accelerates down, and the block on the right accelerates up. The mass of each block is given in the figure. You are going to compare the acceleration and the tension in the string in each system. Which statements are true?

True False The tension is the smallest in C
True False  The tension is the greatest in C
True False  The acceleration is the same in all cases
True False  The tension in A is smaller than that in C
True False  The acceleration in D is greater than that in F

Explanation / Answer

Case A

Equation of motion for both blocks

2g - TA = 2aA

TA - g = aA

Solving both we get

aA = g/3

TA = 4g/3

Case B

using above formula

aB = g/2

TB = 3g

Case C

aC = g/3

TC = 8g/3

Case D

aD = 2g/3

TD = 13g/3

Case E

using above methods

aE = g/3

TE = 4g

Case F

aF = 2g/3

TF = 28g/3

Hence

False - The tension is the smallest in C

False - The tension is the greatest in C

False - The acceleration is the same in all cases

True - The tension in A is smaller than that in C

False - The acceleration in D is greater than that in F

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