A roller coaster heads into a circular loop with radius 5m .
If the 2000 kg coaster is moving at 10 m/s at the top of the loop, what is the magnitude of the normal force that the track applies to the coaster in N?
At the top of the loop, the net force is directed toward the center of the circular path and is given by the centripetal force:
Fc = mv² / r
where Fc is the centripetal force, m is the mass of the coaster, v is the velocity, and r is the radius of the loop.
Given:
m = 2000 kg
v = 10 m/s
r = 5 m
Plugging in these values into the formula:
Fc = (2000 kg)(10 m/s)² / 5 m
= (2000 kg)(100 m²/s²) / 5 m
= 400,000 N
Therefore, the magnitude of the normal force that the track applies to the coaster is 400,000 N.