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Work Energy Theorem problem: Dealing with Gravitational Force on a hanging man

by dgibbs
Tags: joules, work energy theorem
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dgibbs
#1
Apr1-12, 10:18 PM
P: 18
1. The problem statement, all variables and given/known data

Spiderman, whose mass is 80.0 kg, is dangling on the free end of a 12.0 m long rope, the other end of which is fixed to a tree limb above. By repeatedly bending at the waist, he is able to get the rope in motion, eventually getting it to swing enough that he can reach a ledge when the rope makes a 60.0 degree angle with the vertical. How much work was done by the gravitational force on spiderman in this manuever?


2. Relevant equations

Work energy Theorem = (Force)(Displacement)




3. The attempt at a solution

So I drew a diagram. I showed that this 80.0 kg spiderman began hanging at 90.0° straight down and then he moved to a 60.0° angle. I showed that the rope was 12 m long.

I then set up the formula. A = 90.0° B = 60.0°
∫ (mg)cos(90.0°-60.0°) =
= (80kg)(9.8m/s)(cos 30.0°)
=392 joules
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ehild
#2
Apr2-12, 01:08 AM
HW Helper
Thanks
P: 10,660
Quote Quote by dgibbs View Post

So I drew a diagram. I showed that this 80.0 kg spiderman began hanging at 90.0° straight down and then he moved to a 60.0° angle. I showed that the rope was 12 m long.

I then set up the formula. A = 90.0° B = 60.0°
∫ (mg)cos(90.0°-60.0°) =
= (80kg)(9.8m/s)(cos 30.0°)

=392 joules
What do you mean with that formula?
How do you calculate work? What force does the Earth exert on Spiderman? What is its displacement? What is the angle between force and displacement?



ehild
azizlwl
#3
Apr2-12, 01:57 AM
P: 963
Maybe you look at conservation force which is relevant to your case.
http://en.wikipedia.org/wiki/Conservative_force


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