Question

A girl ties a rope securely to the windowswill of a tower and climbs down to the base of it. She is with a group of friends and wants them to come down too, but easier. She ties the other end of the rope to a tree 30m down and 60m away horizontally, creating a zipline. The first person down the zipline weighs 80 kg. Draw a free body diagram of the forces on this person, and how great is the force of tension in the rope while he zips down?

Answer 1

Given

w: weight

w = 80 kg

T: Tension

T = ?

Procedure

Free body diagram

First we must calculate the angle formed between the tension and the horizontal. To calculate this angle we can use the information we were given about the horizontal and vertical distances of the zipline.

`\begin{gathered} \tan a=(30)/(60) \\ a=26.56^(\circ) \end{gathered}`

Now we can do the summation of forces on the y-axis to calculate what is the value of the string tension. We are assuming that the rope is frictionless.