A 3.00- m -long, 270- N , uniform rod at the zoo is held in a horizontal positio

Question

A 3.00-m-long, 270-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends. The left rope makes an angle of 150 ? with the rod and the right rope makes an angle ? with the horizontal. A 91-N howler monkey (Alouatta seniculus) hangs motionless 0.50 m from the right end of the rod as he carefully studies you.

A) Calculate the tension in the left rope.

B) Calculate the tension in the right rope.

C) Calculate the angle

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A 3.00-m-long, 270-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends. The left rope makes an angle of 150 ? with the rod and the right rope makes an angle ? with the horizontal. A 91-N howler monkey (Alouatta seniculus) hangs motionless 0.50 m from the right end of the rod as he carefully studies you Calculate the tension in the left rope. Calculate the tension in the right rope. Calculate the angle

Explanation / Answer

Sum of the forces:
1) Tl*sin30 + Tr*sin A = 270 + 91 = 361 N and
2) Tl*cos30 = Tr*cos A

Sum of the moments about the left end of the bar:
3) Tr*sin A*3 = 270*1.5 + 91*2.5 = 632.5 N?m or
4) Tr*sin A = 632.5/3 = 210.83 N

Substituting this value in 1)
.5*Tl + 210.83 = 361
Tl = 300.34 N ------------------ (a)

Substituting in 2)
5) 300.34*cos30 = Tr*cos A
Tr*cos A = 260.10

Dividing 5) into 4)
tan A = 210.83/260.10
A = 39.03 degree ----------------- (c)

and using 4)
Tr*sin A = 210.83 N
Tr = 334.8 N ------------------- (b)

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