Question 150300
For problems describing variation of one thing compared to something else, you can derive the formula yourself.
Here's how:
Let F = force, W = car's weight, S = car's speed, and R = radius of curvature.
You can write:
{{{F = kWS^2/R}}} The force, F, varies jointly (and directly) as the the car's weight, W, and the square of the car's speed, S, so W and S go on top and inversely as the radius, R, of the curve, so R goes on the bottom.
Note that since this is variation problem, it is not correct to say that the force, F, equals the right side, so you must use a constant of variation, and that's the k in the formula.
Now you can substitute the given numbers for F =(3600 pounds), W = (1800 pounds), and S = (20 mph), and (R = 600 ft.) to find the value of k.
{{{3600 = k(1800)(20)^2/600}}}
{{{3600 = k(1800)(400)/600}}} Simplify.
{{{3600 = k(1200)}}} Divide both sides by 1200.
{{{3 = k}}}, so now the formula becomes:
{{{F = 3WS^2/R}}}
Now substitute the second set of numbers for W = 1800, S = 50mph, and R = 570 ft.
{{{F = 3(1800)(50)^2/570}}}
{{{F = 3(1800)(2500)/570}}}
{{{F = 23684}}}pounds of force.