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?

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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.

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