Solving for Upward Acceleration: Using a Basic Pulley System

[eatingblaa]

1. To hoist himself into a tree, a 67.2-kg man ties one end of a nylon rope around his waist and throws the other end over a branch of the tree. He then pulls downward on the free end of the rope with a force of 361 N. Neglect any friction between the rope and the branch, and determine the man's upward acceleration.
2. f=ma3.I thought that the amns weight at the other end would be

67.2(9.81) = 659.232N

and this would make an overall force of 298.232 but not up, down,

this would give an acceleration of -4.42 ms-2

but this is wrong

any help?

 

[Doc Al]

Hint: How many places does the rope pull on the man?

 

[eatingblaa]

ah okay two different places never thought of it like that,

okay so now I am thinking that his weight is split between both his waist and arm,

659.232 /2 = 329.616N

361 - 329.616 = 31.384 N that are free to pull himself vertically,

a =f/m =31.384/27.4 = 1.145 ms-2

I hope this is right, thank you, I also just thought a lot more about what this question meant, he would have been getting awful rope burn dropping at 4.42 ms-2 :)

 

[eatingblaa]

damn still wrong, have no idea

 

[Doc Al]

That's an interesting way of looking at it, but you made a few errors. Try this:

What upward forces act on the man? Downward forces? What's the net force?

Apply Newton's 2nd law to find the acceleration.

 

[eatingblaa]

Okay let's see,

Upward forces:

pulling down on the rope @ 361 N

tension in the rope @ ?

Downward forces:

weight of the man @ 67.2 x 9.81 = 659.232 N

 

[Doc Al]

Upward forces:

pulling down on the rope @ 361 N

tension in the rope @ ?

All we care about are forces on the man. But if the man pulls on the rope with a force of 361 N, what must be the tension in the rope? And how many time does that tension pull up on the man?

Downward forces:

weight of the man @ 67.2 x 9.81 = 659.232 N

 

[eatingblaa]

tension in the rope would be 361 N and would be on both sides? so cancel each other out?

so the only forces on the man are his weight and pulling himself up?

sorry if I am missing something completely, I feel like there is still something to click with me in this question

 

[Doc Al]

tension in the rope would be 361 N and would be on both sides?

Yes, the tension in the rope is 361 N, and the tension is the same at both ends of the rope.

so cancel each other out?

Why would they cancel out? The rope pulls up twice. So the upward force is twice the tension.

so the only forces on the man are his weight and pulling himself up?

Gravity (his weight) is a downward force on the man. When he pulls down on the rope, the rope pulls back on him--twice. (But all we care about when trying to find the man's acceleration are the forces on the man. Sure, he also exerts forces on the rope, but we don't care.)

 

[eatingblaa]

okay so upward forces on the man are the tension on the rope caused by the man pulling one side, these are 361 x 2 = 722 N

downward forces is his weight caused by gravity = 659.232 N

Net Force = 62.768

a = 0.934 ms-2 ?

sorry for being so slow tonight

 

[Doc Al]

Looks good!

 

[eatingblaa]

thanks for all the help, now i just need to figure out my other question posted down lower,

and how to mark this as done