# the *answer*

Your variables are: mass m = 70.3 kg, pendulum height d = 6.24 m g = local gravitational constant = 9.8 N/kg.

The "trick" to this problem is to realize that the potential energy you must have at the point of release (the top of the pendulum arc) is entirely converted to kinetic energy at the moment the pendulum swings through the bottom of its arc. This is the moment of most rapid centripetal acceleration and therefore the moment the passenger on the carpet ride will feel the greatest force. The potential energy at the point of release = m g d equate this with kinetic energy for a mass of 70.3 kg (0.5 m v^2) i.e., m g d = 0.5 m v^2 to get the maximum velocity. Thus v = square root (2 g d). Now from this velocity you can determine the centripetal acceleration. You must know the radius of the pendulum itself (this works for roller coasters, too, if you can find the radius of the circle which matches the curvature of the bends in the track). Centripetal acceleration equals v^2 / r for acceleration along a circle of radius r. If this is also the pendulum height d (i.e., you are dropped so you are instantaneously in free fall) then the formula is quite simple: centripetal acceleration = (sqrt(2 g d)) ^ 2 / d = 2 g d / d = 2 g As you correctly observed, there's also the extra g contributed by the Earth (it doesn't turn off) so the participant would feel 3 g of force at the bottom of the ride.

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