In the ride shown, a person A sits in a seat that is attached via a cable of length L to a...

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 mB. The total mass of the person and the seat is mA. The trolley is constrained by the beam to move only in the horizontal direction. The rider is released from rest at the angle θ = θ0 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 equations needed to find the velocity of the trolley and the rider for any arbitrary value of θ. Clearly label all equations and list the corresponding unknowns, showing that you have as many equations as you have unknowns. Solve the equations for the unknowns, and then plot the velocity of the trolley and the speed of the rider as a function of the angle θ for both halves of a full swing of the rider. Use WA = 100 lb, WB = 20 lb, L = 15 ft, and θ0 = 70°.

Figure P5.38