A 57.0 kg person in rollercoaster moving through the bottom of a curved track of radius 42.7 m feels a normal force of 995 N. How fast is the car moving?

Answer 1

The person experiences two forces -- force of gravity and the centrifugal force.

At the bottom of the track both forces are aligned, pointing downward.

I am assuming that 995N refers to the combined force.

The force of gravity, being mass times gravitational acceleration, is

57 kg x 9.8 m/s² = 558.6 N.

Therefore the centrifugal force is 995 N - 558.6 N = 436.4 N.

The formula for centrifugal force is

F = mv²/r

From that get expressing v:

v = sqrt(rF/m)

Substituting actual numbers

v = sqrt(42.7 m x 436.4 N / 57 kg) = 18 m/s