physics questions about normal wieght

Question

a car is going over the top of a curvature approximates a circle of radius 91m. Of what velocity will the occupants of the car appear to weigh 24% less than their normal weight or their normal weight times 0.76.

Answer 1

At the top if the curve, the occupants of the car are accelerating downward with a_c = v² /R  where v is the velocity and R = 91 m  ((centripetal acceleration)

  

The free body diagram for an occupant shows two forces:  1) , the downward force of gravity = mg  where m is the mass of the occupant and g = 9.81 //s²  ( the acceleration due to gravity) ; 2) N,  the upward force of the car seat on the occupant (this is sometimes called the normal force).   Newton's second law ( F = ma) is then

 

mg -    N =  m v² /R

 

It turns out that N is what a person perceives as his/her effective weight.   So N = .76 x normal weight = .76 mg

 

Plugging this in for N and solving for v gives

 

 v = sqrt ( .24 R g)  = 14.63 m/s