Finding work for this problem

[crhscoog]

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?

 

[Redbelly98]

How much more energy does Batman have at the end of the process, compared to at the beginning? Where would that energy come from?

 

[baba89]

I would first check the units to ensure they are consistent and use the correct formula for work. In this case, the units for force should be in Newtons (N) and the distance should be in meters (m). So, the correct formula for work would be W= F*d*cos(theta).

Next, I would double check the given information to make sure all the values are correct. It is important to note that the angle given is not the angle between the rope and the vertical, but rather the angle at which Batman reaches the ledge. To find the angle between the rope and the vertical, we can use the trigonometric relationship, cos(theta) = adjacent/hypotenuse.

In this case, the adjacent side is the length of the rope (16m) and the hypotenuse is the distance from the tree limb to the ledge, which we can calculate using trigonometry. This would give us an angle of approximately 82.4 degrees.

Plugging in the correct values, we get:

W= (101kg*9.8m/s^2)*(16m)*cos(82.4 degrees)
= 2647.6 J

Thus, the work done against the force of gravity in this maneuver is approximately 2647.6 J. It is important to double check the units and make sure the angle used is correct in order to get an accurate answer.