My Notes Ask Your Tea 2,0 A piñata of mass M 13 kg hangs on a rope of negligible

Question

My Notes Ask Your Tea 2,0 A piñata of mass M 13 kg hangs on a rope of negligible mass that is strung between the tops of two vertical poles. The horizontal distance between the poles is D 2.9 m, the top of the right pole is a vertical distance h-0.55 m higher than the top of the left pole, and the total length of the rope between the poles is L 3.96 m. The pirata is attached to a ring, with the rope passing through the center of the ring. The ring is frictionless, so that it can slide freely along the rope until the piñata comes to a point of static equilibrium. (a) Determine the distance from the top of the left (lower) pole to the ring when the piñata is in static equilibrium. (b) What is the tension in the rope when the piñata is at this point of static equilibrium?

Explanation / Answer

Given,

M = 13 kg ; D = 2.9 m ; h = 0.55 m ; L = 3.96 m ;

a)3.96 sin(theta) = 2.27

theta = sin^-1(2.27/3.96) = 35 deg

2 x sin35 + h tan35 = 2.27

1.15 x + 0.55 x tan35 = 2.27

x = 1.64 m

Hence, x = 1.64 m

b)2T cos(theta) = mg

T = 13 x 9.8/2 x cos35 = 77.76 N

Hence, T = 77.76 N

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