A 3.00-m-long, 280-N, uniform rod at the zoo is held in a horizontal position by

Question

A 3.00-m-long, 280-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 93-N howler monkey (Alouatta seniculus) hangs motionless 0.50 m from the right end of the rod as he carefully studies you.

Part A

Calculate the tension in the left rope.

Express your answer using two significant figures.

Part B

Calculate the tension in the right rope.

Express your answer using two significant figures.

Part C

Calculate the angle?.

Express your answer using two significant figures.

Explanation / Answer

Statics
sum of forces in h and v directions must = zero
sum of all moments about any point must = zero

If we choose to sum moments about the left end of the rod, the vertical component of the right rope tension may be found
Once we have the right vertical component, we can sum forces in the vertical direction to get the left vertical component.
With the left vertical component, we can find the tension in the left rope and thus the horizontal component of the left tension
Summing horizontal tensions to zero will give us the right rope horizontal tension. We then can figure the whole right rope tension and the angle on which it works.

Sum of moments. Assume CW positive. Origin at left end of rod. Fvr is Force vertical right

280(1.5) + 93(2.5) - Fvr(3.0) = 0
Fvr = (280(1.5) + 93(2.5)) / 3
Fvr = 217.5 N

Summing vertical forces. Fvl is Force vertical left. Up is positive
Fvl - 280 - 93 + 217.5 = 0
Fvl = 155.5
Fvl/T = sin150
T = Fvl / sin150
T = 155.5 / 0.5 = 311 N in left rope ======= ANS A)

Horizontal Force due to left rope
311 cos 150 = -269.33 = Fhl

Summing horizontal forces
Fhl + Fhr = 0
Fhr = -Fhl
Fhr = 269.3

Tension comes form adding component vectors
sqrt (269.3^2 + 217.5^2) = 346.16 N ========= ANS B)
angle is
inv tan 217.5 / 269.3 = 38.9 degrees = theta ===== ANSC)

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