Please answer A and B If possible explain thank you very much in advance! A rope

Question

Please answer A and B If possible explain thank you very much in advance!

A rope has mass density sigma (sigma= M/L, where M is the mass of the rope and L is the length). The rope lies in a heap on the floor. You grab one end and pull straight up at constant speed v. a) What force must you apply, as a function of the height y that your end is above the floor? (Assume no knots or kinks, the rope comes straight up when you pull.) b) Does your answer make sense? How does it behave when y is very small and then increases to be large? You should get two terms in your answer: what, physically, does each one represent? Say something intelligent.

Explanation / Answer

Here ,

mass density of rope is sigma

a)

height of rope y , y < L

mass of rope of length y , m = sigma * y

as the rope is pulled with constant speed

Force applied = m *g

Force applied = sigma * y * g

for y > L

Force applied = m *g

Force applied = sigma * y * L

b) yes the answer make sense.

when y is very small , force is nearly zero

when y is large , force becomes m *g * L

two terms represent that the force is constant after a value of y

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