Asked by EMMA
a 100kg street light is supported equally by two ropes. one rope pulls up and to the right 40 degrees above the horizontal; the other pulls up and to the left 40 degrees . what is the tension of the rope?
Answers
Answered by
Henry
M*g = 100kg * 9.8N./kg = 980 N. = Wt. of
st. light.
T1*Cos(180-40) + T2*Cos40 = -980*cos270.
-0.766T1 + 0.766T2 = 0.
0.766T2 = 0.766T1.
T1 = T2.
T1*sin(180-40) + T2*sin40 = -980*sin270.
0.643T1 + 0.643T2 = 980.
Replace T2 with T1:
0.643T1 + 0.643T1 = 980.
1.286T1 = 980.
T1 = 762 N. = T2.
st. light.
T1*Cos(180-40) + T2*Cos40 = -980*cos270.
-0.766T1 + 0.766T2 = 0.
0.766T2 = 0.766T1.
T1 = T2.
T1*sin(180-40) + T2*sin40 = -980*sin270.
0.643T1 + 0.643T2 = 980.
Replace T2 with T1:
0.643T1 + 0.643T1 = 980.
1.286T1 = 980.
T1 = 762 N. = T2.
Answered by
Henry
Or T1 = T2.
T1*sin(180-40) + T1*sin40 = -980*sin270.
0.643T1 + 0.643T1 = 980.
1.286T1 = 980.
T1 = 762 N. = T2.
T1*sin(180-40) + T1*sin40 = -980*sin270.
0.643T1 + 0.643T1 = 980.
1.286T1 = 980.
T1 = 762 N. = T2.
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