How Much Work Does Batman Do Swinging to a Ledge?

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SUMMARY

The discussion focuses on calculating the work done by Batman while swinging on a 16 m rope to reach a ledge at an 80.4-degree angle with the vertical. The correct formula for work is W = Frcos(theta), where F is the gravitational force (mass times acceleration due to gravity). The initial calculation of 2641.08 J is incorrect due to an improper angle usage. The correct angle for the calculation should be derived from the swing's vertical displacement.

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  • Understanding of basic physics concepts such as gravitational force and work.
  • Familiarity with trigonometric functions, specifically cosine.
  • Knowledge of the formula for work: W = Frcos(theta).
  • Basic understanding of energy conservation principles.
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  • Review the derivation of angles in pendulum motion to accurately calculate vertical displacement.
  • Study the concept of gravitational potential energy and its relation to work done against gravity.
  • Explore the effects of different angles on the work done in swinging motions.
  • Learn about energy conservation in mechanical systems, particularly in swinging objects.
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Homework Statement



Batman, whose mass is 101kg, is holding on to the free end of a 16 m rope, the other end of which is fixed to a tree limb above. He is able to get the rope in motion as only Batman knows how, eventually getting it to swing enough that he can reach a ledge when the rope makes a 80.4 degree angle with the vertical. The acceleration for gravity is 9.8m/s^2. How much work is done against the force of gravity in this maneuver? Answer in units of J.

Homework Equations



W= Frcos(theta)

The Attempt at a Solution



W= Frcos(theta)
= (101*9.8)(16)(cos80.4)
= 2641.08 J
= wrong answer

What am I doing wrong? From the looks of it, maybe the angle? If so what angle do I use and how do I find it?
 
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How much more energy does Batman have at the end of the process, compared to at the beginning? Where would that energy come from?
 

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