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 200pounds of force keeps a 3200-pound car from skidding on a curve of radius 400ftat 25mph. What force would keep the same car from skidding on a curve of radius 550ftat 55mph?

Question
Asked Jul 30, 2019
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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
200

pounds of force keeps a
3200

-pound car from skidding on a curve of radius
400
ft

at
25
mph

. What force would keep the same car from skidding on a curve of radius
550
ft

at
55
mph

?

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Expert Answer

Step 1

Given: The Force (F) that is needed to keep a car from skidding on a curve varies inversely as the radius (r) of the curve, and jointly as the weight (w) of the car and square of the car’s speed (s).

ws2
that can be written as
Thus, the relation obtained from the given infomation is Fa
kws
F =
k is a constant
r
400 ft and s 25 mph
It is supposed that F = 200 pounds, w=3200 pounds
help_outline

Image Transcriptionclose

ws2 that can be written as Thus, the relation obtained from the given infomation is Fa kws F = k is a constant r 400 ft and s 25 mph It is supposed that F = 200 pounds, w=3200 pounds

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Step 2

In order to obtain the force that would keep the same car on a radius of 550 ft at 55 mph, assume w as constant.

Ks
-, K is a constant.
Thus, the formula ofF can be writtenas F =
r
help_outline

Image Transcriptionclose

Ks -, K is a constant. Thus, the formula ofF can be writtenas F = r

fullscreen
Step 3

Obtain the value of ...

K (25)
2
200
400
200.400
K =
625
K 8.16
K 128
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K (25) 2 200 400 200.400 K = 625 K 8.16 K 128

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