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A old massless rope of 12 meters attached to a ceiling can sustain a maximum tension force of 1200N before breaking. An 85 kg person climbs up the rope. What is the minimum possible time in which he can climb to the top without breaking the rope?

My issue is figuring out the forces involved as the person climbs up the rope.
would there be an applied force downward, because the person must push down to climb up the rope? Or is that not counted because the person always weighs the same? So would it be:
Fgravity + FApplied = Fmax tension?

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  • $\begingroup$ Is the rope massless? $\endgroup$
    – BMS
    Commented Mar 24, 2014 at 21:58

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It sounds like your rope is massless (since its mass/density/similar information is not given). Think about a free-body diagram (force diagram) for the person. It's pretty simple, right? Gravity acting straight down, and an upward force from pulling on the rope. The acceleration of the person will depend on how big that upward force is (and gravity). That upward force on the person has to come from somewhere, and the only reasonable conclusion here is that it must come from increasing the tension in the rope...

Once you can relate the tension in the rope and the acceleration of the person, the rest should be a straightforward kinematics problem.

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  • $\begingroup$ Kyle is right. You need to connect the person's acceleration to the tension in the rope. This is done via Newton's 3rd law. $\endgroup$
    – BMS
    Commented Mar 24, 2014 at 22:02
  • $\begingroup$ Curious side issue: if the rope were not massless, the time could approach zero. Just treat the rope as reaction mass, not a means of support... $\endgroup$
    – DJohnM
    Commented Mar 25, 2014 at 18:13

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