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?
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 !
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.