SOLUTION: 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 fo

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Question 203746: 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 36 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 curce of radius 570 feet at 50 mph?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First write the formula:
F+=k%28WS%5E2%2FR%29 where:
F = The required force, k = the constant of proportionality, W = car's weight in lbs, S = the speed of the car, in mph., and R = the radius of curvature in feet
To find k, make the appropriate substitutions of the given parameters:
F = 36 lbs.
W = 1800 lbs.
S = 20 mph.
R = 600 feet.
36+=+%28k%2A%281800%29%2820%29%5E2%29%2F600 Multiply both sides by 600.
21600+=+k%2A%281800%29%28400%29
21600+=+k%2A%28720000%29 Divide both sides by 720000.
k+=+0.03
Now the formula is:
F+=+%280.03%28WS%5E2%29%29%2FR Substitute: W=1800lbs, S = 50mph, and R = 570 feet.
F+=+%280.03%281800%29%2850%29%5E2%29%2F570 Evaluate.
F+=+135000%2F570
highlight%28F+=+236.84%29lbs.