A car with a mass of 1200 kg is moving around a circular curve at a uniform velocity of 20 meters per second. the centripetal force on the car is 6000 newtons. what is the radius of the curve?

F = m v^2 / r

r = m v^2 / F

r = 1200 * 400 / 6000 = 120 * 4 / 6 = 20 * 4 = 80

Units are left as an excersise.

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!