Question

Calculate the tension in the two ropes if the person is motionless. Person weighs 76kg and 15 degree angle rope one and 10 degree angle rope 2

Answer 1

M*g = 76 * 9.8 = 745 N.=Wt. of person.

T1*Cos(180-15) + T2*Cos10 = -745*cos270.
-0.966T1 + 0.985T2 = 0.
T2 = 0.981T1

-500i + T1*sin(180-15) + T2*sin10 = 0.
Replace T2 with 0.981T1:
-500i + T1*sin165 + 0.966T1*sin10 = 0.
-500i + 0.259T1 + 0.168T1 = 0.
-500i + 0.427T1 = 0.
0.427T1 = 500i.
T1 = 1172i = 1172N.[90o].
T2 = 0.981*1172i = 1149i = 1149N[90o].

Answer 2

Correction:

M*g = 76*9.8 = 745 N. = Wt. of person.

T1*Cos(180-15) + T2*Cos10 = -745*Cos270.
-0.966T1 + 0.985T2 = 0.
T2 = 0.981T1.

-745 + T1*sin(180-15) + T2*sin10 = 0.
Replace T2 with 0.981T1:
-745 + T1*sin(180-15) + 0.981T1*sin10=0.
-745 + 0.259T1 + 0.170T1 = 0.
-745 + 0.429T1 = 0.
0.429T1 = 745.
T1 = 1735 N.
T2 = 0.981 * 1735 = 1702 N.