Question 150300: The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car's speed, and inversely as the radius of the curve. If a force of 3600 pounds is needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet what force would be required to keep the same car from skidding on a curve of radius 570 feet at 50 mph? Round your answer to the nearest pound of force?
I don't know the formular for this one and thus don't know how to solve it.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! For problems describing variation of one thing compared to something else, you can derive the formula yourself.
Here's how:
Let F = force, W = car's weight, S = car's speed, and R = radius of curvature.
You can write:
 The force, F, varies jointly (and directly) as the the car's weight, W, and the square of the car's speed, S, so W and S go on top and inversely as the radius, R, of the curve, so R goes on the bottom.
Note that since this is variation problem, it is not correct to say that the force, F, equals the right side, so you must use a constant of variation, and that's the k in the formula.
Now you can substitute the given numbers for F =(3600 pounds), W = (1800 pounds), and S = (20 mph), and (R = 600 ft.) to find the value of k.
 Simplify.
 Divide both sides by 1200.
 , so now the formula becomes:
Now substitute the second set of numbers for W = 1800, S = 50mph, and R = 570 ft.
 pounds of force.
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