A 3.00-m-long, 300-N, uniform rod at the zoo is held in a horizontal position by

Question

A 3.00-m-long, 300-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends (the figure (Figure 1) ). The left rope makes an angle of 150 ? with the rod and the right rope makes an angle ? with the horizontal. A 96-Nhowler 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 ?.

A 3.00-m-long, 300-N, uniform rod at the zoo is held in a horizontal position by two ropes at its ends (the figure (Figure 1) ). The left rope makes an angle of 150 degree with the rod and the right rope makes an angle Theta with the horizontal. A 96-Nhowler 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. TL= N Calculate the tension in the right rope. TR= N Calculate the angle Theta. Express all answers to 2 significant figures.

Explanation / Answer

Sum of the forces:
1) Tl*sin30 + Tr*sin A = 300 + 96 = 396 N and
2) Tl*cos30 = Tr*cos A

Sum of the moments about the left end of the bar:
3) Tr*sin A*3 = 300*1.5 + 96*2.5 = 690 N?m or
4) Tr*sin A = 690/3 = 230 N

Substituting this value in 1)
.5*Tl + 230 = 396
Tl = 332 N ------------------ (a)

Substituting in 2)
5) 332*cos30 = Tr*cos A
Tr*cos A = 287.52

Dividing 5) into 4)
tan A = 230/287.52
A = 38.656degree ----------------- (c)

and using 4)
Tr*sin A = 230 N
Tr = 367.412 N ------------------- (b)

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