Centripetal Force

OBJECTIVES:

  1. To find out how centripetal force is related to velocity, mass, and radius of the circular path.
  2. To determine the m/r ratio for an object undergoing circular motion.

INTRODUCTION:

If no net force acts upon a moving object, it will travel in a straight line with no change in speed. To cause an object to travel in a circular path, a force constantly perpendicular to the direction of motion must act upon the object. This force, called the centripetal force, will always be directed toward the center of the circle.

During this experiment you will determine the relationship between the centripetal force acting on an object and the speed of the object as it travels its circular path when the radius of the circular path followed by the object is kept constant.

METHOD:


A rubber stopper will be made to move in a horizontal circular path by means of whirling it from one end of a dacron cord. The centripetal force necessary for the stopper’s motion will be provided by weights of known mass suspended from the other end of the cord. To ensure that only the weights provide the force (instead of the hand doing the whirling), the cord will be passed through a glass tube which will be held by the experimenter.

The mass of the stopper may be determined by measuring it on a balance. The radius of the circular path should be measured from the top of the glass tubing to the stopper’s center of mass. To ensure that the radius remains constant (1.00 m), use a felt-tip marker to mark the cord approximately one centimeter below the tubing. As the stopper is whirled, the distance between the tubing and mark should remain at 1 cm.

Five different masses will be suspended from the cord, starting with approximately 50 g and increasing in 50 g increments. The speed with which the topper must be whirled to maintain the constant one-meter radius will depend on the suspended mass. The speed of the stopper will be determined by measuring the time for 30 complete revolutions of the stopper. After the time for one complete revolution has been calculated, the speed may be found by dividing distance by time, where distance is the circumference of the circle.

DATA:

Suspended Mass (kg) / Suspended Weight (N) / Time for 30 Rev. (s) / Time for One Rev. (s) / Circumference (m) / Speed (m/s)

Measured Mass of Stopper: ______kg

Measured Radius of Circular Path: 1.00 m

Measured Mass/Radius Ratio: ______kg/m

DATA TREATMENT:

  • Suspended weight
  • Speed of stopper
  • Include any additional calculations required to answer specific interpretations/analysis of errors questions with the answers to those questions
  • Be sure to include both graphs (curve and linear).

INTERPRETATIONS:

  1. Plot a graph of centripetal force (suspended weight) versus speed. Describe the resulting curve. What function of speed appears to vary directly with force?
  1. Plot the graph which you think will give a linear relationship (force versus some function of speed). According to this straight line, what function of speed varies directly with force (F  Does this support the form of the equation for centripetal force given in the text?
  1. Determine the slope of the graph in #2. According to the equation for centripetal force, what should the slope of this graph be equal to? Show why.
  1. What would happen to the stopper's speed if its mass were doubled by tying two stoppers to the string (assume the radius and suspended weight remain constant)? If its original speed were 5.0 m/s, what would its new speed be? Justify your answer.
  1. What would happen to the stopper's speed if the radius of its path were made four times longer (assume the stopper's mass and the suspended weight remain constant)? If its original speed were 5.0 m/s, what would its new speed be? Justify your answer.

ANALYSIS OF ERROR:

  1. Calculate the %error between the slope in #3 and the actual value based on the stopper's mass and the radius of the circular path.
  1. How might have friction between the glass tube and fishing line contributed to error in this experiment?