Question

A 114 kg man balances on a rope between two walls.
Each half of the rope makes a different angle relative to horizontal as shown.
In this case, angle θL = 71 degrees while angle θR = 25 degrees.
(A) What is the tension in the left side of the rope?
(B) What is the tension in the right side of the rope?

Answer 1

Use
\[{\sum} Fx=0\ and\ {\sum} Fy=0\]

Let
Tl=Tension of rope on left, and
Tr=Tension of rope on right
tl=angle on left
tr=angle on right
g=acceleration due to gravity

Then
Tl sin(tl)+Tr sin(tr) - 114g = 0 ...(1)
Tl cos(tl) - Tr cos(tr) = 0 ...(2)

tl and tr are known numberical values, so substitute in (1) and (2) to solve for Tl and Tr.