between the negatively charged electron and the positively charged nucleus. The contrast in length scales between planetary orbits, with radii on the order of 102 m, and atomic orbits, with radii on the order of 1010 m, is worthy of note. On more moderate length scales, in human affairs, tire friction provides the centripetal force which moves a car in a circular path. And an object swung around overhead (for example, a lasso) does so in response to the centripetal force provided by the tension in the rope. Substituting the expression for centripetal acceleration, 1. derived in your textbook, into Newton's second law, F-ma, one finds an expression for the centripetal force: my F. The mass, m, and the radius of motion, r, are each directly measurable quantities. After measuring the object's period T (the time required for one complete revolution) the velocity can be determined from the relation v= di = 2/T. Substituting this expression for v into the expression for Fe gives F. In this lab, a spring's tension provides the centripetal force. You will measure m, r, and T, and use Eq. (3) to find Fe from them. Since the spring's tension is a function of the length to which it is stretched, you can compare Fe as calculated above, with a more direct measurement of the same force. Draping a string over the pulley, the hanging mass that stretches the spring to the same length that the rotating bob did must have a weight equal to Fo The comparison between the directly measured force (the weight used in the static approach) and the value of Fe found from Eq. 3 will be the bottom line in your calculations. 33 Procedure J1. Weigh your object and record its mass on the data sheet under Trial 1 Mass. v2. For your first trial, set the vertical "marker rod" as close as possible to the axis of rotation. When set into circular motion, the bottom point of the object should pass directly over the marker rod. 3. Measure the distance from the center of the marker rod to the center of the axis of rotation, and record this on the data sheet under Trial 1 Radius. 4. Adjust the horizontal boom so that the strings from which the object hangs will lie in a vertical plane. Tighten both the marker rod and the boom in place. Note that the strings upward tension will then cancel the downward gravitational force on the object. Also balance the apparatus by adjusting the counterweight so that the whole system rotates smoothly. 6. Reattach the spring and turm the rotor just fast enough so that the bob passes directly over the marker rod. After some practice at giving the mass a reasonably uniform speed, you will find that you are pushing a tiny amount each revolution in order to compensate for frictional losses. As always, practice and patience are your keys to good honest data. 7. Determine the period T(the time for each revolution) by dividing the time for 20 revolutions by 20. Record this on the data sheet under Trial 1 Period. 8. Use your experimental values of m r, and Tin Eq. (3) to calculate the centripetal force, and enter this value in the appropriate box on the data sheet. Show your work in the space provided on the data sheet. 9. Directly measure the spring's force by stretching it to the same extension it had when rotating. Do this by attaching some hanging masses on a string draped over the premounted pulley, which is used merely to redirect the downward force of gravity. If the spring is stretched to the same length as when it was spinning, the weight of the hanging masses (mg) should equal the centripetal force to within experimental error. Record this on the data sheet under Trial 1 Directly Measured Force. 10. Reset the marker rod to the largest radius of its range, and repeat steps 1 through 9 two more times, for your second trial. 11. For the third trial add a 100 g flat weight on top of the mass, and leave the radius unchanged from that of trial 2. 34