Posted by Matthew Goldberg on Friday, June 15, 2012 at 9:07pm.
Assume that car tires and shock absorbers do not "cushion" the bump, so that the passenger's center of mass follows the profile of the bump.
The apparent weight is the force that the seat applies to the person to keep him or her in place. At the top of the bump, less force is required because there is a downward centripetal acceleration.
The person's actual weight is M g = 645.8 N
That gets reduced by
M V^2/R = 262.2 N
temporarily, due to the bump
The apparent weight is then 383.6 N
The centripetal acceleration is down, toward the center of the circle
Ac = v^2/R = 11.7^2/34.4 = 3.98 m/s^2
The gravity force down on driver = m g = 65.9*9.8 = 646 Newtons
The force up on the driver from the car is F, the weight a scale would measure if placed on the seat.
so
total force down on driver = m (Ac)
646 - F = 65.9 (3.98)
F = 646 - 262
F = 384 Newtons
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