Problema Solution
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 travelling 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 570 feet at 50 mph? Round your answer to nearest pound of force.
Answer provided by our tutors
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 travelling 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 570 feet at 50 mph? Round your answer to nearest pound of force.
F1 = 3600, M1 = 1800, V1 = 20MPH, R = 600ft
R = 570 FT, V = 50 MPH
F = MV^2/R
M = FR/V^2
M is constant for the car.
So, we can equate the cases.
We get :
3600*600/400 = x*570/2500 = 23684 Pounds