Question
Find the tension in each of the two ropes supporting a hammock if the first one is at an angle of 19.4° above the horizontal and the second is at an angle of 35.3° above the horizontal. The person sleeping in the hammock (unconcerned about tensions and ropes) has a mass of 60 kg.
Answers
Henry
M*g = 60 * 9.8 = 588 N. = Wt. of the person.
Eq1: T1*Cos9.4 + T2*Cos35.3 = 0.
T1*Cos9.4 = -T2*Cos35.3.
T1 = -0.827T2.
Eq2: T1*sin9.4 + T2*sin35.3 =-588[270o].
0.1633T1 + 0.578T2 = 0 + 588
Replace T1 with -0.827T2:
0.1633*(-0.827T2) + 0.578T2 = 588
-0.135T2 + 0.578T2 = 588
0.443T2 = 588.
T2 = 1327 N.
T1 = -0.827T2 = (-0.827)*1327 = -1098 N.
Eq1: T1*Cos9.4 + T2*Cos35.3 = 0.
T1*Cos9.4 = -T2*Cos35.3.
T1 = -0.827T2.
Eq2: T1*sin9.4 + T2*sin35.3 =-588[270o].
0.1633T1 + 0.578T2 = 0 + 588
Replace T1 with -0.827T2:
0.1633*(-0.827T2) + 0.578T2 = 588
-0.135T2 + 0.578T2 = 588
0.443T2 = 588.
T2 = 1327 N.
T1 = -0.827T2 = (-0.827)*1327 = -1098 N.