A block with mass 'M' is attached to the lower end of a vertical, uniform rope with mass 'm' and length 'L'. A constant upward force 'F' is applied to the top of the rope, causing the rope and block to accelerate upward. Find the tension in the rope at a dstance 'x' from the top end of the rope, where 'x' can have any value from 0 to 'L'.
Newton's Second and Third Laws.
The Attempt at a Solution
I'm a bit confused on this question. I've tried breaking the problem up into three parts - one for the block mass 'M', one for the top of the rope and one for a point 'x' on the rope - but I can't seem to get it to work. The actual constant force there is annoying too - for the top of the rope I have a force acting downwards of (m+M)g, and an upwards force that is greater than that of 'F', but I don't know how I can equate etc. The answer is F[M+m(1-x/L)]/(M+m) but I want to know why.
Thanks in advance.