During a stage production of Peter Pan, the 56-kg actress playing Peter has to f

Question

During a stage production of Peter Pan, the 56-kg actress playing Peter has to fly in vertically (descend). To be in time with the music, she must, starting from rest, be lowered a distance of 2.8 m in 1.9 s at a constant acceleration. Backstage, a smooth surface sloped at 50

During a stage production of Peter Pan, the 56-kg actress playing Peter has to fly in vertically (descend). To be in time with the music, she must, starting from rest, be lowered a distance of 2.8 m in 1.9 s at a constant acceleration. Backstage, a smooth surface sloped at 50 degree supports a counterweight of mass m, as shown below. What mass of the counterweight must the stage manager use? kg What is the resulting tension in the wire? kN

Explanation / Answer

(b) If T is the tension in the wire, then net force down on Peter is
. . . F = mg - T
and he accelerates
. . . F = ma = mg - T
over a distance
. . . x = 1/2 at^2
. . . a = 2x / t^2
. . . T = mg - ma = mg - (2mx / t^2) = 56(9.81-2(2.8/(1.9)^2)) = 462.5 N

(a) Backstage, the mass M on exerts a force down of Mg, with a force parallel to the inclined ramp of
. . . Mg sin(50deg) = T = mg - (2mx / t^2)

=> M*9.81(0.766) = 462.5

= > M = 61.5Kg

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