Question

A 57.0 kg person in a

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

Answer: 18.1 m/s

Explanation:

Answer 2

The linear speed of the car is approximately 27.30 m/s

Step-by-step explanation:

The question parameters are;

The mass of the person on the rollercoaster, m = 57.0 kg

The radius of the rollercoaster track, r = 42.7 m

The normal force felt by the person, F = 995 N

The centripetal force acting on the person keep the circular motion is given by the following equation;

`Centripetal \, force \ F_c = (m * v^2)/(r)`

Where;

v = The linear velocity of motion = The linear speed of the car

The centrifugal force, F, is the force normal force felt by the person and is equal to the centripetal force, therefore, we have;

`Centripetal \, force \ F_c = Centrifugal \, force \ F = (m * v^2)/(r)`

From which we have;

`F = 995 = (57 * v^2)/(42.7)`

`\therefore v = \sqrt{(995 * 42.7)/(57) } \approx 745.38`

The linear speed of the car = v ≈ 27.30 m/s

The angular speed of the car, ω = v/r ≈ 27.30/42.7 ≈ 0.639 rad/s