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 poundforce 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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 12000.
F ∝ w, F ∝ v2, and F ∝ 1/r
F = × k
⇒ 6125 = × k
⇒ k = (6125 × 550)/(2750 × 1225)
⇒ k = 1
According to the question,
⇒ F = (3600 × 50 × 50 × 1)/750
⇒ F = 240 × 50 = 12000