4 Significant figures In the ride shown, a person A sits in a seat that is attac

Question

4 Significant figures

In the ride shown, a person A sits in a seat that is attached via a cable of length L to a freely moving trolley B of mass m B. The total mass of the person and the seat is m A. The trolley is constrained by the beam to move only in the horizontal direction. The system is released from rest at the angle theta = theta 0 and it is allowed to swing in the vertical plane. Neglect the mass of the cable and treat the person and the seat as a single particle. Determine the velocities of the trolley and the rider the first time that theta = 0 degree. Evaluate your solution for W A = 98 lb, WB = 21 lb, L = 17 ft, and theta 0 = 70 degree. The velocity of rider is ( ) and the velocity of the trolley is ( )

Explanation / Answer

0.5*Ma*Va^2 = Ma*g*h

Va = sqrt(2*g*h) = sqrt(2*g*L*(1-cos70)) = sqrt(2*32.1522*17*(1-cos70))

Va = -26.8195 i ft/s


Ma*Va + Mb*Vb = 0

Mb = +Ma*Va/Mb = (26.8195*98)/21= 125.1577 i ft/s

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