Solve the problem.
-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 3600 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 curve of radius 700 feet at 30 mph? Round your answer to the nearest pound of force?
A)7513 lb
B)6811 lb
C)6975 lb
D)6943 lb

Question

Quizplus · Accepted Answer

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^2 $, and inversely as the radius of the curve $ R $. This relationship can be expressed as $ F = k \cdot \frac{W \cdot S^2}{R} $, where $ k $ is the constant of variation. Given $ F = 3600 $ pounds for $ W = 1800 $ pounds, $ S = 20 $ mph, and $ R = 600 $ feet, we can solve for $ k $ and then use it to find the force required for $ W = 1800 $ pounds, $ S = 30 $ mph, and $ R = 700 $ feet. The calculation yields a force of approximately 6943 pounds, rounding to the nearest pound.

Solve the Problem. -The Force Needed to Keep a Car from Skidding on from Skidding