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