What Happens When a Monkey Pulls on a Rope with a Weight on the Other Side?

[borku1]

Homework Statement

A weightless rope is draped over a frictionless pully attached to the ceiling (change of direction only, no mechanical advantage). Attached to one end of the rope is a 5 kg weight sitting in the floor. A 5 kg monkey grabs the other end of the rope and begins to pull down on the rope.
Does:
a) the monkey rise off the floor,
b) the 5 kg weight rise up off the floor, or
c) both the monkey and the weight rise off the floor at the same rate.

Homework Equations

This is a question from a mechanics section of the high school physics book i had in the early 60's (algebra & trig, no calc). Since this question has stuck with me all these years, i would appreciate a pointer to what concept or equations i should consider.

The Attempt at a Solution

thanks in advance

 

[tiny-tim]

Welcome to PF!

Hi borku1! Welcome to PF!

Hint: if the monkey is pulling down, the tension in the rope will increase.

 

[borku1]

i agree, and i believe the tension would be the same on the 5kg monkey and 5kg weight. For instance, after the monkey first establishes 5kg tension on the rope, and then, by further pulling on the rope, shortens it by 2 meters, one or both of the monkey and weight will be a total of 2 meters up off of the floor. And i believe the potential energy of either end system (monkey up 2 meters, weight up 2 meters, or both up 1 meter) will be the same.

The force the monkey applies to the rope could equally:
accelerate the monkey's mass by 'x', or
accelerate the weight's mass by 'x', or
accelerate both his mass and the weight's mass (10kg) by 1/2 'x' (half the acceleration), moving both off the floor an equal amount.

so, i guess i miss the point of tension as a hint. How would the tension lead us to select one scenario over the other?

thanks again in advance

 

[willem2]

The tension of the rope and the force of gravity are the only forces on the monkey, and on the weight, since the tension is the same on both sides of the pulley ...

 

[tiny-tim]

… How would the tension lead us to select one scenario over the other?

Call the tension T (as willem2 says, it's the same on both sides of the pulley), and do F = ma separately for the monkey and for the 5 kg weight.

What do you get?​