# Physics

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A 50.0-kg 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.

• Physics -

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

• Physics -

2Tsin15=mg=0
2Tsin15=mg
T=mg/(2sin15)
T=(50)(9.8)/(2sin15)

• Physics -

T=490/(2sin15)
T=490/.517
T=948

• Physics -

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

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