Does the mechanical advantage change if the load applies force?

[Levi R]

Hello, I am here to ask if anyone would help answer a question for me, in regards to a simple pulley system. The question is, does the mechanical advantage of a system change if the load is also the what is applying force to the system? Thank you for any answer you choose to give.

 

[Levi R]

To explain a bit more: The system in the photo is generally accepted to offer a 2:1 MA. My question is: would the MA of this system be changed if the load were a climber who also was putting the effort into the system. Thanks!

 

[anorlunda]

Your question sounds confusing. It sounds like you are saying that the pulley is stayed to the load and nothing else. Isn't it started to a fixed point also?

 

[Levi R]

Thank you for the welcome and apologies for the confusion.

Imagine that the "load" in the above image were a person and that person was also providing the force to the effort leg of rope. Would this still be a 2:1 MA?

 

[anorlunda]

If the other person's feet pushed on the floor, the answer is different. If the other person just rides in the box, his weight acts link a fixed weight.

But a person in the box could hoist himself up by pulling where the first person pulled. The 2:1 mechanical advantage still applies.

 

[Levi R]

Thank you.

 

[Levi R]

Does anybody care to agree or disagree with the above statement? Personally I agree however I have run into a large body of individuals who asserts that if the load does the hauling then somehow this system turns to a 3:1 MA. Thanks.

 

[jbriggs444]

Does anybody care to agree or disagree with the above statement? Personally I agree however I have run into a large body of individuals who asserts that if the load does the hauling then somehow this system turns to a 3:1 MA. Thanks.

You are correct, @anorlunda is incorrect (or is answering an unintended question).
If you are hanging from beneath the pulley and are also pulling downward on the rope, the tension in all three lengths of rope (you to upper pulley, upper pulley to lower pulley and lower pulley to fixed point) are equal and all three are supporting you. The simple algorithm of counting the lines works and computes a mechanical advantage of three to one.

 

[anorlunda]

@jbriggs444 was right. I counted wrong.

 

[Khashishi]

To understand why, remember that a machine trades between force and distance that you pull the rope. If you are riding on the load, you move up while the rope moves down, so the distance you pull the rope is effectively longer (in your frame of reference) for the same amount of rise.