Riders in an amusement park ride shaped like a Viking ship hung from a large piv

Question

Riders in an amusement park ride shaped like a Viking ship hung from a large pivot are rotated back and forth like a rigid pendulum. The pendulum can rotate a full 360 degree. At one point in the ride, the ship is momentarily motionless at the top of its circular arc with the pendulum arm in the horizontal position. The ship then swings down under the influence of gravity. Assuming negligible friction, find the speed of the riders at the bottom of its arc, given the system's center of mass travels in an arc having a radius of 12.9 m and the riders are near the center of mass. What is the centripetal acceleration at the bottom of the arc? Find the normal force exerted by the ride on a 61.0 kg rider at the bottom of the arc. What is the ratio of the force to her weight? Force = Ratio =

Explanation / Answer

a: The system will lose potential energy through a height equal to the radius.
At the bottom, with neglible friction this will be convertec to kinetic energy.
PE = KE
mgh = ½mv²
gh = ½v²
2gh = v²
v = (2gh) = (2 * 9.8m/s² * 12.9m) = 15.90 m/s

b. Centripetal force: Fc = mv²/r

ma = mv²/r
a = v²/r = 15.902 / 12.9 = 19.6 m/s²

c.

Normal force = total downward force
N = ma

N = 61*19.6 = 1195.6

Actual weight = mg

ratio:
ma/mg = a/g = 19.6 / 9.8 = 2

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