This is problem 3 in Chapter 7 of Serway\'s Physics forScientists and Engineers,

Question

This is problem 3 in Chapter 7 of Serway's Physics forScientists and Engineers, 7th Edition: Batman, whose mass is 78.0 kg, isholding onto the free end of a 13.0 mrope, the other end of which is fixed to a tree limb above. He isable to get the rope in motion as only Batman knows how, eventuallygetting it to swing enough that he can reach a ledge when the ropemakes a 62.0°angle with the vertical. How much work was done by thegravitational force on Batman in this maneuver? In the solution provided on the website, the work done by thegravitational force on Batman is calculated to beW=(mg)(dr)(cos180) where the angle is in degrees, dr ends up being6.89 meters, and mg is the force of gravity on Batman(764.4N). Why is the angle used in the calculation here 180 and not theangle 62 that was given in the problem?
This is problem 3 in Chapter 7 of Serway's Physics forScientists and Engineers, 7th Edition: Batman, whose mass is 78.0 kg, isholding onto the free end of a 13.0 mrope, the other end of which is fixed to a tree limb above. He isable to get the rope in motion as only Batman knows how, eventuallygetting it to swing enough that he can reach a ledge when the ropemakes a 62.0°angle with the vertical. How much work was done by thegravitational force on Batman in this maneuver? In the solution provided on the website, the work done by thegravitational force on Batman is calculated to beW=(mg)(dr)(cos180) where the angle is in degrees, dr ends up being6.89 meters, and mg is the force of gravity on Batman(764.4N). Why is the angle used in the calculation here 180 and not theangle 62 that was given in the problem?

Explanation / Answer

Here the force of gravity is downward and hence his verticaldisplacement contributes to work. Therefore                 W = mgy Where y = L ( 1 - cos) is the vertical distance from the meanposition.               W = m g L ( 1 -cos )                    = 78 * 9.8 * 13 ( 1 - cos62)                    = 5271.96 J

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