Follow the instructions and answer the questions.

Lab: Whirled on a String, Centripetal force and circular motion Objective: To find the mass of a ball while exploring the relationship between tangential velocity and circular motion as well as centripetal force and centripetal acceleration. CAUTION: each student, particularly the "Twirler", should be careful of his/her surroundings so as not to cause injury to one's self or another. Materials List: PVC tube, string-ball set up, stop watch, hanging masses, meter stick, scale Procedures: 1. Feed the free end of the string through the PVC tube. 2. Hook a small (50 g or less) mass to the free end. 3 . Grasp the PVC tube vertically in one hand; whirl the ball (not the mass!) above your head in a(n approximately) horizontal circle. Adjust the rate of rotation so that the radius of the circle is parallel to the floor and is constant (i.e., the hooked mass does not drop or rise). 4. In a data table, record the mass, radius of the circle and the average time for one circle of the ball. 5. Repeat #2-4 for each student in the group. Analysis: 1. Draw two sketches of the ball -mass system, a top view and a side view. 2. Draw a FBD of the ball -mass system. Label the v, a and F vectors. 3 . Calculate the tangential speed of the ball, show a sample calculation in an Appendix. 4. What are the centripetal acceleration and centripetal force for each observation? Show a sample calculation in an Appendix. 5. If the radius of the circle were not parallel to the floor (i.e., there is a "sag angle"), how does your FBD change? How do v, a and F vectors change? Draw the new FBD including the "sag angle". 6. Calculate the mass of the ball. 7. Use the scale to measure the mass of the ball. Conclusions: 1. Derive the relationship (equation) between hanging mass and ball velocity; include "sag angle"-the angle below the horizontal. 2. What is the calculated mass of the ball? Compare the calculated vs. measured ball mass. Explain with several sentences the difference, if any