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LAB 7 Centripetal Force and Torque OBJECTIVES 1. To study the acceleration of and forces on an object moving in a circular path. 2. Use Newton’s 2nd Law given by F = mv2/R to predict the period of a rotating object. EQUIPMENT Glass tube, stopper on a string, stopwatch, and weights THEORY An object following a circular path is acted upon by a centripetal force. The centripetal force is the name given to the net force required to keep an object of mass m, moving at a speed v, in a circular path of radius r. Newton’s 2nd law states that F maC m v2 , r PROCEDURE Part 1: Centripetal Force and Acceleration a. Using a “whirly gig” (a system made of a glass rod, rubber stopper, hanging mass and string), whirl the stopper over your head at a constant speed so the 50g mass stays fixed at about eye level and the glass tube stays within the marks on the string. b. Have your partner measure the time for 10 - 20 revolutions and determine the experimental period Texpt for one revolution. Repeat several times and then change partners. Repeat until you have at least 15 values of Texpt. f. From your 15 values for the period, calculate the average period Tavg and standard deviation σT. Express your results as Texpt = Tavg ± σT. g. Use Newton's 2nd law to calculate the period (Tthy) of the rotating stopper as a function of the hanging mass mh, the mass of the stopper ms, the radius of the circular path R, and the acceleration due to gravity g. h. Setup and draw the confidence interval Texpt ± σT. Is Tthy consistent within one standard deviation of the experimental measurements? Why or why not? What were some possible sources of error? Part 2: Torques in Static Equilibrium In this lab assume that all torques are balanced: torques 0 r1 F1 r2 F2 { { torque 1 torque 2 and that the definition of the lever arm is a. Arm Torque The bicep muscle attaches to the lower arm near the elbow joint. When it flexes, it exerts a torque on the lower arm. Our model uses a spring scale to represent the bicep. Slide the attachment to different places and use the scale to hold the arm in a horizontal position. Record the force in the ‘muscle’ and the lever arm. Is the torque a constant as the lever arm is increased? Questions Where is the force the greatest? Where is it the smallest? If you were to design the ‘perfect’ bicep, where would you attach the muscle/tendon - why? Using rough measurements of your arm, make an estimate of how much force your bicep has to exert (in lbs) when you have a 10 lb. bowling ball in your hand. c. Door Push ‘Tug-o-War’ How many students are required to push at the 1/3-mark (of the door width) to counteract another student pushing in the oppose direction at the door knob? d. Estimate your Mass First balance a wood plank (affectionately called Max) on the pivot. Then use a 20.4 kg mass and Max to estimate you weight (mg)thy (in Newtons). Compare (mg)thy with (mg)actual (from the bathroom scale) using a percent difference. How do they compare?