6. Circular Motion Cwslar motion occurs in nature when an object experiences a net force (and therefore an accelenation) directed towands the center of the circle. Apparatus The hand powered centripetal force apparatus consists of a smoothly rotating central rod on a support base, a marker rod, an adjustable boom with a counterweight attached, a bob, a pulley, and a spring. The device is used to measure the centripetal force supplied by its own spring as described below. You will also have the use of a scale, a ruler, some string, and a stopwatch. Mess Figure 1: Apparatus Physical Principles Newton's second law explains that whenever a mass undergoes an acceleration, it does so in response to a net force. An object moving with a constant speed in a circular path is accelerating, since the vector representing its velocity is continually changing. That is, although the vector's magnitude is constant (in the case of "uniform" circular motion), its direction is most definitely not constant. In fact, the object 1S continually accelerating inward, towards the center of the circle around which it moves. This can be seen graphically by subtracting the vector representing the object's velocity at one particular moment from the vector representing its velocity at a slightly later moment, as shown in Figure 2. 31 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