Answer:
98.952≅ 99 N
Explanation:
Since you don't know the tension in the cable 0.63 m from the watermelon, use this as your axis.
Clockwise moments:
(245)(2.32)
This is the weight of the scaffolding, acting in the middle of the board.Since we took the cable as the axis, instead of 3.25 m as the distance, it's 2.15 m, the distance from the cable to the middle of the board.
Counterclockwise moments:
(T)(5.27) + (7.6)(9.8)(0.63)
The other cable and the weight of the watermelon.
These need to be equal to each other.
(T)(5.27) + (7.6)(9.8)(0.63) = (245)(2.32)
Solving for T, and you should get 98.952≅ 99 N
The tension is in the cable at the end of the scaffolding is 99 N.
The tension in the cable is determined by applying Principle of moment. That is the sum of the clockwise moment is equal to sum of the anticlockwise moment.
Middle of the cable = ¹/₂ x 5.9 = 2.95 m
Position of the cable before the middle = 5.9 m - 0.63 m = 5.27 m
Take moment about the second cable at the end position.
Clockwise moment = anticlockwise moment
(7.6 x 9.8 x 5.9) + (245 x 2.95) = T₁5.27
1162.18 = T₁5.27
T₁ = 1162.18/5.27
T₁ = 220.5 N
The sum of the upward force must be equal to downward force
T₁ + T₂ = (7.6 x 9.8) + 245
T₁ + T₂ = 319.5
T₂ = 319.5 - T₁
T₂ = 319.5 - 220.5
T₂ = 99 N
Thus, the tension is in the cable at the end of the scaffolding is 99 N.
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