Centripetal Force Objective: The objective of this experiment is to measure the force needed to keep a mass rotating around in a circular path. In this experiment this force will be provided by a spring which stretches to allow the mass to rotate in a circle of known radius. Also the student will measure the period of rotation and from it calculate the centripetal force predicted by theory and compare it with the measured result. Introduction: A movement on a circular path with constant speed Vo requires a net force that keeps the moving object on the circular path. The centripetal acceleration of a movement on a circular path of radius R is directed towards the center of curvature of the circular path with the magnitude: acp (1) Rem The centripetal force is therefore - which is a net force: Fop . = Myol R (2) Apparatus: Pasco Centripetal Force apparatus, weight hanger and weights, photogate, LabPro and a computer. side post center post assembly string assembly clamp-on rotating pulley mass platform Flag for photogate Grip for hanging rotation "A" base mass Figure 1: Rotation apparatusExperiment Procedure: 0. The procedure consists of two steps each experiment: (1) Measuring the force under static conditions with a weight hanging across a pulley, and (2) re- establishing the balance position with the hanging mass removed while the mass is rotating by bringing the red tab back into the reference ring. 1. Attach a piece of cardboard to the free end of the rotating platform for the photogate to detect when it passes through (see figure 1): The photogate will not be used to measure the speed, but to count to ten rotations, measure the period time, and take an average. 2. Now place the photogate such that the flag blocks and unblocks the beam as the mass rotates. Open the Logger Pro folder and open the Pendulum Timer or Centripetal Force file. The computer will measure the period of rotation. 3. Set the outer edge of the center post . assembly to 9.0 cm on the center post right side (where the flag is). This is string assembly needed because of the fixed length of the string and the limited range of the spring. When changing the radius, as the radius gets larger, 9 cm mark this post needs to be moved - to 5 cm - as you will find necessary. Flag for photogate 4. Select a radius - in the first round it should be 10 cm - by setting the Figure 2: center post positioning side post (see figure 1) to the desired position by aligning the line on the side post with the desired position on the measuring tape. While pressing down on the side post to assure that it is vertical, tighten the thumb screw on the side post to secure its position. Record the radius in the data table. 5. A rotating mass of NOMINALLY 200 g should 50g masses (2) already be hanging from the side post. Unhook the rotating object from the three strings. Measure the mass of the rotating object using the digital 100g mass with 3 open balance, and record-it in the data table. Re-attach hooks the three threads to the three hooks in the mass as shown in figure 1. Figure 3: Rotating mass assembly 6. Attach the clamp-on pulley to the end of the track nearer to the side post. Attach a string to the hanger (remember it has a mass of 5. g!) over the clamp-on pulley. Add mass for a total of mh = 50 g.7. The object on the side bracket must hang spring bracket center vertically: On the center post, adjust the spring post bracket vertically (see figure 1) until the string from which the object hangs on the side post is indicator aligned with the vertical line on the side post. spring disk When finished, align the indicator bracket on the center post with the orange indicator (see indicator figure 3). This will be your reference. bracket 8. Now remove the hanging mass and the Figure 3: Spring assembly pulley from the rotating platform. The mass will now be pulled by the spring to the side and the indicator disk is raised. During the experiment the rotation will bring the mass back to the vertical - as indicated by the indicator disk being back in the indicator bracket. The person rotating the device needs to concentrate on keeping this disk within the indicator bracket. 9. One of the lab partners will start to rotate the apparatus by hand, increasing the speed until the orange indicator is centered in the indicator bracket on the center post. This indicates that the string supporting the hanging object is once again vertical and thus the hanging object is at the desired radius. Another lab partner will - when a stable rotation is achieved - start the timing process by clicking on the start button and time 11-15 rotations or until the period time has stabilized for 10 rotations - then hit the stop button. 10. Highlight ten. consistent measured periods and use the program to calculate the average period of rotation; enter it in your data table. The 10 measured periods should be very close to each other. If there is more than a ~5 % variation, the run should be repeated. 11. Repeat procedures 4-11 for four. more measurements (total 5) and record the data in the data table. 12. Now set your radius to r = 18 cm (it should be there already - and the center post should be at 5 cm) and keep it there for the next set of experiments. Repeat procedures 4- 11 for a total of five measurements each with the hanging mass increased from 30g in steps of 20 g up to 110 g and record the data in the data table. Since the radius does not change, the indicator bracket will not have to be adjusted, but the spring and red indicator will need to be re-adjusted for each measurement. IRev = 0.255 = T = period for one cycle Analysis: 4 1. Calculate the weight of the hanging mass for each run. This weight is equal to the centripetal force 2. Calculate the speed of the rotating mass from the equation wlangular speed)Experiment Data Table - Varying Radius Rotating Total Mass in Kg: mrot = 0.2083 kg Hanging Mass in kg: mi = 0.50 kg Radius R Average Speed v Centripetal Centripetal Weight of Difference [cm] Period T [m/s] Acceleration Force Fop Hanging [%] [s] ace [m/s2 ] [N] Mass [N] 10.0 1.38 0.45 2.07 0.43 0.49 13.0 12.0 1.34 0.56 2.63 0.55 0.49 11.5 14.0 1.49 0.59 2.48 0.52 0.49 6.0 16.0 1.58 0.64 2.53 0.53 0.49 7.1 18.0 1.70 0.67 2.46 0.51 0.49 4.2