Answer to Question #160309 in Classical Mechanics for Alex Kingston

Question

A slack rope walker balances on a rope tied between two trees. For a short, he is not moving. His mass is 72 KG. The rope makes an angle of 22 degrees with the horizontal on either side . What is the magnitude of the Tension in the rope ?

Answer 1

$\text{external forces acting on the system:}$

$F_{net}=mg\text{ the force of gravity}$

$T_1,T_2 \text{ directed in different directions along the rope}$

$\text{to the suspension points}$

$\text{due to the symmetry of the system, the values of }$

$T_1\text{ and }T_2 \text{are equal }T_1=T_2$

$\text{the system is in equilibrium therefore the projections of the forces on the axis are 0}$

$F_{net y}=T_{1y}+T_{2y}$

$F_{net y}=F_{net}$

$T_{1y}=T*\sin\alpha$

$T_{2y}=T*\sin\alpha$

$T=\frac{Fnet}{2*\sin{\alpha}}=\frac{mg}{2*\sin{\alpha}}=\frac{72*9.8}{2*\sin22^0}\approx 941.8$

Answer:941.8 N