Question : The force (in pound-force) needed to keep a car from skidding on a curve varies directly with the weight of the car (in pounds) and the square of its speed (in miles per hour [mph]) and inversely with the radius (in feet) of the curve. Suppose 6125 pound-force is required to keep a 2750 pound car, travelling at a speed of 35 mph, from skidding on a curve of radius 550 feet. How much pound-force is then required to keep a 3600-pound car, travelling at a speed of 50 mph, from skidding on a curve of radius 750 feet?
Option 1: 11960
Option 2: 12150
Option 3: 12240
Option 4: 12000
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Correct Answer: 12000
Solution :
The force ($F$) needed to keep a car from skidding on a curve varies jointly as the weight of the car ($w$) and the square of the car's speed ($s$) and inversely as the radius of the curve ($r$).
$F = k[\frac{ws^2}{r}]$
Given: Force of 6125 pounds is needed to keep a 2750-pound car traveling at 35 mph from skidding on a curve of radius 550 feet.
⇒ $6125 = k[\frac{2750\times{35^2}}{550}]$
$k = 1$
Equation:
$F = 1[\frac{ws^2}{r}]$
⇒ $F = 1[\frac{3600\times{50^2}}{750}]$
⇒ $F = 12000$ pound-force
$\therefore$ 12000 pound-force is then required to keep a 3600-pound car, travelling at a speed of 50 mph, from skidding on a curve of radius 750 feet.
Hence, the correct answer is 12000.
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