Find Accelerations & Forces for Astronauts Alex & Bob Pulling a Rope

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Discussion Overview

The discussion revolves around a physics problem involving two astronauts, Alex and Bob, who are pulling on a rope in free space. Participants explore the implications of their differing strengths and how this affects the forces and accelerations involved. The conversation touches on concepts of tension, force exertion, and the conditions under which these forces are measured.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that using impulse leads to the conclusion that Fa = Fb, which contradicts the problem's premise.
  • Another participant argues that since Fa > Fb is given, the net force should be calculated based on the weaker astronaut's force, Fb.
  • A different viewpoint emphasizes that the tension in a massless rope is equal to the force exerted by the weaker astronaut, thus both astronauts experience a force of Fb.
  • Concerns are raised about the problem's wording, questioning whether it misleads by stating that each astronaut pulls as hard as they can when the weaker astronaut's strength limits the force exerted.
  • One participant shares an anecdote from a lab experiment to illustrate the dynamics of unequal pulling forces, suggesting that the stronger astronaut's force does not double the total force exerted on the rope.
  • Another participant critiques the problem's definition of "maximum force," suggesting that it lacks clarity regarding the conditions under which it was measured.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the problem. Multiple competing views remain regarding the forces exerted by the astronauts and the implications of the problem's wording.

Contextual Notes

Participants highlight limitations in the problem's assumptions, such as the definition of maximum force and the conditions under which it is measured, which may not align with the scenario of astronauts in free space.

Rockman000
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two astronauts initially at rest in free space, pull on either end of a rope. Astronaut Alex played football in high school and is stronger than astronaut Bob, whose hobby was chess. The maximum force with which Alex can pull, Fa, is larger than the maximum force with which Bob can pull, Fb. Their masses are Ma and Mbi, and the mass of the rope, Mr, is negligible. Find their accelerations and forces if each pulls on the rope as hard as he can.

Thanks in advance for the help
 
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This is easily solvable in two steps:

1. Pay attention in class
2. Read the textbook
 
Trust me, I've paid a lot of attention in class and read what text we have. If I use impulse, I can prove that Fa = Fb. This generates an answer, however, the fact that Fa = Fb contradicts the problem. Another approach would be to find the difference in the two forces Fa - Fb. Set that to the force and find acceleration by diving that by Ma + Mb (the total mass)
 
I don't see how impulse enters into it at all. Fa > Fb, that is given in the problem.

Your last approach (find the NET force and use it to find the total acceleration of the system) sounds about right.
 
the tension in the rope

It's a bit of a trick question. You can only pull a rope with a force equal to the tension in the rope, and a massless rope has a single tension throughout. Since the weaker Bob can only supply a force of Fb, that's the most the tension can be. So both astronauts are pulled with a force of Fb.

Note that a massless rope merely transfers force between the two astronauts. From Newton's 3rd law you know that whatever force Bob exerts on Alex, Alex exerts equal and opposite on Bob.
 
Turns out, the answer is, Fa + Fb (for the force). but why? :confused:
 
Rockman000 said:
Turns out, the answer is, Fa + Fb (for the force). but why? :confused:
We did this in a lab once using a small girl and a big guy on skateboards. When both pulled, the guy pulled so hard the girl wasn't really pulling at all - her arms stayed extended. So the force was just the larger of the two.

I don't see how it could be Fa+Fb.
 
Doc Al said:
It's a bit of a trick question. You can only pull a rope with a force equal to the tension in the rope, and a massless rope has a single tension throughout. Since the weaker Bob can only supply a force of Fb, that's the most the tension can be. So both astronauts are pulled with a force of Fb.

Note that a massless rope merely transfers force between the two astronauts. From Newton's 3rd law you know that whatever force Bob exerts on Alex, Alex exerts equal and opposite on Bob.

Ok, so isn't the problem being misleading when it says that each astronaut pulls on the rope as hard as he can, when in fact each astronaut pulls on the rope only as hard as the weaker guy can?
 
russ_watters said:
We did this in a lab once using a small girl and a big guy on skateboards. When both pulled, the guy pulled so hard the girl wasn't really pulling at all - her arms stayed extended. So the force was just the larger of the two.
I know what you mean russ, but in this context the girl was "pulling" (that is, exerting a force on the rope) exactly as much as the guy was. If she wasn't, then she couldn't hang on to the rope. (Ignoring the mass of the rope, that is.)
I don't see how it could be Fa+Fb.
Agreed. What if two guys of equal strength pulled on the rope ends with force F? Would the force be 2F? Nonsense.
 
  • #10
cepheid said:
Ok, so isn't the problem being misleading when it says that each astronaut pulls on the rope as hard as he can, when in fact each astronaut pulls on the rope only as hard as the weaker guy can?
That's why I said that this is a bit of a trick question. It turns out that under these conditions, the most that they can pull happens to be equal to the grip strength of the weaker astronaut. :smile:

Actually, the problem statement is tricky at many levels. What does "maximum force" that each can exert even mean? Under what conditions was it measured? Standing on ground pulling a horizontal rope attached to a wall? (And thus relying on friction with the ground.) A more relevant measure would be: have each astronaut stand on a frictionless pad and then pull on a rope attached to the wall as hard as they could. (Lot's of luck.) The maximum tension generated would in some sense measure their relative strength under conditions relevant to the actual problem.

So, on further thought, this problem is very misleading. I wouldn't use it.
 
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