Question

An 80-kg clown sits on a 20-kg bike on a tightrope attached between two trees. The center of mass of the clown is 1.6 mabove the rope, and the center of mass of the bike is 0.70 mabove the rope.

a. A load of what mass should be fixed onto the bike and hang 1.70 m below the rope so that the center of mass of the clown-bike-load system is 0.50 m below the rope?

b. What is the force that the rope exerts on each tree if the angle between the rope and the horizontal is 13 ∘?

Answer 1

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(a)

using principle of moments

Mh = m1h1 + m2h2 + m3h3

(80+20+m) x 0.5 = mx1.7 - 80x1.6 - 20 x 0.7

solving for m

m = 160 kg

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b)

Total mass = 80+20+160 = 260 kg

total weight = 260 x 9.8 = 2548 N

Fy = 0

2T*sin13 - W = 0

2T*sin13 = 2548

T = 5663.45 N

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