Spiderman, whose mass is 72.0 kg, is dangling on the free end of a 11.4-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 ? = 60.8
work done is maximum change in potential energy =
mg L (1-cos A)
=72*9.8*11.4(1-0.4878)
=4123.78 joules
Work done here equals the change in
potential energy,
so does not matter what reference you take to measure the change in
distance....
Work done = m*g*H ... where H is the change in height .. you dont
need an absolute height in this case...
Work done = m*g* (R - R cos(60.8)) ... that's
it...
you can also verifi this...assume that the end of rope where batman
hangs initially is at a distance D1 from the ground...then the the
distance after swinging is D1 + (r- r cos(60.8))..
so change in height is D1 + (R-
Rcos(60))
- D1 = (R- Rcos(60.8))
work done by the gravitational force= -mgL(1-cos(60.8))
=-72*9.81*11.4*(1-0.4878)
= -4124.46 J
Spiderman, whose mass is 72.0 kg, is dangling on the free end of a 11.4-m-long rope,...