Use the graphing calculator to study how the centripetal force varies with changes in the speed with which the object is swung in a horizontal circle, the mass of the object, or the radius of the horizontal circle.

1. How the magnitude of the centripetal force varies with speed:
   In the formula for centripetal force, the force is dependent upon the speed of the object.
   
   The independent variable is the speed v; the dependent variable is the force F.
   The formula can be written for the graphing calculator and entered into "y₁="
   y = (m * x²) / r
   Substitute numerical values for the radius r and the mass m. Graph the function. Use the trace key to determine the value of the force (y) for various values of the speed (x).

   How the magnitude of the centripetal force varies with mass:

   In this case, the independent variable is the mass (m).

   The formula can be written for the graphing calculator and entered into "y₁="

   y = (x * v²) / r

   Substitute numerical values for the radius r and the speed v. Graph the function. Use the trace key to determine the value of the force (y) for various values of the mass (x).

   How the magnitude of the centripetal force varies with radius:

   In this case, the independent variable is the radius (r).

   The formula can be written for the graphing calculator and entered into "y₁="

   y = (m * v²) / x

   Substitute numerical values for the speed v and the mass m. Graph the function. Use the trace key to determine the value of the force (y) for various values of the radius (x).