Physics
posted by Jim on .
A 50.0kg person takes a nap in a backyard hammock. Both ropes supporting the hammock are at an angle of 15.0degrees above the horizontal. Find the tention of the ropes.

Draw a free body diagram. Then perform a static force balance.

2Tsin15=mg=0
2Tsin15=mg
T=mg/(2sin15)
T=(50)(9.8)/(2sin15) 
T=490/(2sin15)
T=490/.517
T=948 
M*g = 50 * 9.8 = 490 N.
Eq1: T1*Cos15 + T2*Cos165 = 0
T1*Cos15 = T2*Cos165
T1 = T2
Eq2: T1*sin15 + T2*sin165 = 490[270].
0.259T1 + 0.259T2 = 0 + 490
Replace T1 with T2:
0.259T2 + 0.259T2 = 490
0.518T2 = 490
T2 = 947 N. = T1