The mass of the car is 413.6 kg
Explanation:
The missing figure related to the problem is in attachment.
Here we have a roller coaster car moving in the loop-the-loop. At point A, there are two forces acting on the car:
- The normal force exerted by the track, upward, N
- The weight of the car, downward, [tex]mg[/tex]
The net force must be equal to the centripetal force (since this is a circular motion), so we can write:
[tex]N-mg = m\frac{v^2}{r}[/tex]
where we have:
N = 20,600 N
m is the mass of the car
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
v = 20.0 m/s is the speed of the car at point A
r = 10 m is the radius of the loop
Solving for m, we find the mass of the car:
[tex]m=\frac{N}{g+\frac{v^2}{r}}=\frac{20600}{9.8+\frac{20.0^2}{10}}=413.6 kg[/tex]
Learn more about circular motion:
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