Well, first of all, the car is not moving with a uniform velocity.
It's on a part of a circle, so the direction of its motion is constantly
changing. Its speed may be constant, but its velocity is constantly
changing, because direction is a big part of velocity.
OK. So its mass is 1200 kg, its speed is 20 m/s, and 6000N of
centripetal force is enough to keep it on a circular path.
The centripetal force on an object moving in a circle is
F = (mass) x (speed)² / (radius)
6,000 N = (1,200 kg) x (20 m/s)² / (radius)
Multiply each side
by (radius): (6000 N) x (radius) = 24000 kg-m²/s²
Divide each side
by (6000 N): radius = (24,000 kg-m²/s²) / (6000 N)
= (24,000 kg-m²/s²) / (6000 kg-m/s²)
= 4 meters .
In the real world, this is an absurd situation. But I think
my Physics and my Math here are OK.
It just says that if you were in a car that weighs 2,645 pounds,
and you were cruising along at 45 miles per hour, then if you
could somehow arrange for a centripetal force of 1,350 pounds,
it would be enough centripetal force to keep your car on a circular
track that's only 26 feet across !
