The total energy is constant. We have enough information at the top to work out what it is. Everywhere else the total is the same, but the split between kinetic and potential energy is different. At point A we know the potential energy (mgr) so we can use the difference between the known total and the known potential to find the kinetic energy at A ((1/2)mu2). Hence we can find the velocity (u) at A. Hence we can find the centrifugal force (mu2/r) at A; this is the only force imposed by the car on the track at this point.
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As far as I can see the only force that the car applies to the track at point A is the normal force.
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well, Now I understood the first part, where you find the mechanical energy at the top
but why you used it at part B while we need the normal force !
The total energy is constant. We have enough information at the top to work out what it is. Everywhere else the total is the same, but the split between kinetic and potential energy is different. At point A we know the potential energy (mgr) so we can use the difference between the known total and the known potential to find the kinetic energy at A ((1/2)mu2). Hence we can find the velocity (u) at A. Hence we can find the centrifugal force (mu2/r) at A; this is the only force imposed by the car on the track at this point.
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