Question 1204635: The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the car's speed. Suppose that 640 pounds of force keeps a 2600-pound car from skidding on a curve of radius 650 at 40 mph. What force would keep the same car from skidding on a curve of radius 750 ft at 30 mph?
Found 3 solutions by josgarithmetic, greenestamps, mananth:
Answer by josgarithmetic(39621)   (Show Source):
You can put this solution on YOUR website! f, the force needed
r, the curve radius
w, the car's weight
s, speed of car
k, variation constant
This is what the description becomes literally, in variables------
Your question gives these as values and asks for so you can determine value for k.
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Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
If you need a formula relating the variables, and/or if you need to find the constant of proportionality, then use the process outlined by the other tutor.
If you only need to answer this question, then there is a much faster path to that answer.
From the first scenario to the second, the radius changes by a factor of 750/650 = 15/13. The force varies inversely as the radius of the curve, so the required force changes by a factor of 13/15.
From the first scenario to the second, the speed changes by a factor of 30/40 = 3/4. The force varies directly as the square of the speed, so the force changes by a factor of (3/4)^2 = 9/16.
From the first scenario to the second, the weight of the car does not change, so there is no change to the required force there.
So from the first scenario to the second the force changes by a factor of (13/15)(9/16).
ANSWER: 312 pounds
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the car's speed. Suppose that 640 pounds of force keeps a 2600-pound car from skidding on a curve of radius 650 at 40 mph. What force would keep the same car from skidding on a curve of radius 750 ft at 30 mph?
F (1/r)(W)(s^2)
F= k * w*s^2/r
640 *650=K *2600*(40)^2
k=0.1
F = 0.1*2600*30^2/750
F=312
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