A student tries to raise a chain consisting of three identical links. Each link

Question

A student tries to raise a chain consisting of three identical links. Each link has a mass of m. The three-piece chain is connected to a string and then suspended vertically, with the student holding the upper end of the string and pulling upward. Because of the student's pull, an upward force of F is applied to the chain by the string. Use Newton's laws to answer the following questions.

Find the acceleration of the chain. Take the free fall acceleration to be g.

Find the force exerted by the top link on the middle link.

Explanation / Answer

Accel of chain:
Given F=MA, A=F/M
the chain weighs 3m so:

a=f/3m (if your looking for the accel the chain feels)
or
a=f/3m - g (if your looking for the accel upwards relative to the room)

The force between the top and middle link is:
F=a*2m
or using the result for a we just computed
F=f/3m *2m=2/3 f

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