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 570 feet at 50 mph? Round to the nearest pound of force.
This is the general formula for all variation problems:
>>...The force needed to keep a car from skidding on a curve varies...<<
This force is the . We will use the letter . So
>>...jointly as the weight of the car and the square of the car's speed,...<<
The are the weight, , and speed, , squared, which gives
>>...and inversely as the radius of the curve...<<
There is just one , the radius .
So we write the equation using the general formula for all
variation problems:
eliminating the ones that don't apply:
>>...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...<<
Plug those values in: ,, ,
Solve for k:
So go back to this equation:
and substitute only the value of
or we can just make it
Now our formula is complete. We are now ready to use it:
>>...what force would be required to keep the same car
from skidding on a curve of radius 570 feet at 50 mph?...<<
That just asks: What is when , , and
So we plug those in:
>>...Round to the nearest pound of force...<<
we round that to the nearest pound.
Edwin