Purpose of the experiment

Transcription

1 Centripetal Force PES 116 Adanced Physics Lab I Purpose of the experiment Determine the dependence of mass, radius and angular elocity on Centripetal force. FYI FYI Hershey s Kisses are called that because the machine that makes them looks like it is kissing the coneyor belt. Centripetal Force - 1

2 Table of Contents Background 3 Lab Procedure 4 Additional Questions 8 Equipment List LabPro Interface Force Sensor with hook Rotary Motion Sensor 295 g calibration mass Rotational platform Centripetal Force Accessories Large Ring stand x2 Ring stand clamps x2 Long metal rod Centripetal Force - 2

3 Background A force that pulls an object toward the center of a circle is called a centripetal force. How much centripetal force needs to be exerted to cause an object to moe in a circle? Your experience should tell you that the amount of centripetal force that you need to exert depends on: 1. The mass of the object you are whirling the heaier the object the more force is needed. 2. How fast you are whirling the mass around going faster requires more force 3. The radius of the circle Now that we hae defined the factors that affect centripetal force we need to come up with an experiment that can test them. This question can t be answered all at once, much like most scientific experiments. Only one ariable should be changed at a time and then measure the effect on the others. The most difficult quantity (between mass, speed and radius) to hold constant from experiment to experiment is the spinning speed of the object. Therefore, we will study the effect of speed on centripetal force since it is relatiely easy to hold the mass of the spinning object and the radius of the circle constant. Let s take a look at how this pans out mathematically. Remember that the 2 1 definition of acceleration is: the time rate of change of the elocity a. The t t elocities and accelerations we are talking about here are ectors (they hae a magnitude and a direction). You change either of these quantities and you change the ector. Usually when you hae acceleration it is because the magnitude (speed) is changing, but you can hae acceleration while holding the speed constant and that s by changing the direction. Like going around a circle at a constant speed. R a R w It can be shown that the magnitude of this acceleration is: 2 ar R Centripetal Force - 3

4 Let s see how we apply this new knowledge by soling the simple problem of spinning a weight held on by a string. We will call the spinning mass (M), the radius of the circular path (R) and the rate at which M completes one rotation is the period (T). Something has to oppose this centripetal force, something that will keep M traeling on its circular path. You might think it is the string, but the string is just the conduit by which the force is transmitted. The force that holds M in its orbit is the hanging mass. We will assume, for this example, that the force due to the hanging mass is exactly equal and opposite of the centripetal force. Now we can apply some thought experiments to our example. What will happen to the radius (R) if we increase the rotational speed? What will need to happen to the alue of the Hanging mass if we increase the rotational speed but want to keep the same radius (R)? Thought experiments are great, but let s look at something more concrete. A close up iew of the apparatus shows that a force sensor is connected to a sliding mass by a cable. This will allow us to measure the Force Sensor centripetal force as the mass is rotated on the platform. Rotating Platform Centripetal Force - 4

5 Let s apply some math. Assume the platform is rotating with an angular elocity of w. The rotating mass plus the sliding mass holder has a mass of M is at a radius of R. The centripetal force (F) is translated along the cable to the force sensor. F F M Newton s laws applied to the spinning mass: F m a F x M R 2 R The linear elocity () is harder to measure in the lab, and besides the Rotational Motion Sensor outputs the angular elocity (w). From lecture you should hae learned that the linear elocity and angular elocity are related through a single equation: = wr Therefore: F = MR w 2 Note: If you plot F s. w 2 this will gie you a nice linear plot with MR as the slope. We will be using the apparatus pictured below to measure effects of speed on centripetal force. You can hold the radius constant and ary the mass and obsere the affect of the centripetal force as a function of the rotational elocity. In the second set of experiments you will ary the radius while holding the mass constant. Centripetal Force - 5

6 The Lab The goal of this lab is to determine the factors affect centripetal force. Part A: Setup 1. Connect the Force sensor to CH 1 on the LabPro. Connect the Rotary Motion Sensor to DIG/Sonic Open the file: PES 116/Centripetal Force.cmbl 3. Calibrate the Force sensor. 4. Weigh the sliding mass holder, screw included. You will add this mass to all future Mass measurements. Return the mass holder to the rotating platform, make sure the loop at the end of the cable is always under any additional masses and that the tick mark is toward the ruler portion of the rotating platform. 5. Use the supplied bubble leel and the adjusting feet to leel the apparatus. Perform a leeling at two different positions of the rotary arm. Repeat this process until you achiee a leel bubble at both locations of the arm. This is ery important so make sure you do a good job. 6. Add whateer mass is necessary to the both mass holders (the fixed mass holder is there to counter balance the rotating platform). Apply just enough pressure to remoe the slack from the cable and note the radius. Adjust the radius by moing the force sensor up or down. For the first set of data pick a radius somewhere around 16 cm. Set the fixed mass to the same radius. The recorded mass (M) is only the combined mass of the brass disks and the sliding mass holder. 7. Position the Force sensor directly oer the pulley. Make sure the rotating arm will not hit the ring stands when rotated. Rotate the arm the arm fast enough to remoe the slack in the cable. Adjust the Force sensor until the ertical section of the cable does not wobble. Any wobble will greatly affect the alue of the data. Centripetal Force - 6

7 8. You should always spin the platform using the section of the rod between the arm and the base. BE CAREFUL that you do not moe the platform or you will need to recalibrate the whole system again. Part B: Measure F s. w 2 1. Make sure you perform all the preparatory steps of Part A to insure the best data possible. 2. Start by adding a 100g mass to both holders. Remember to record the total mass of the sliding mass, M. 3. Rotate the arm with a elocity somewhere around 10 rads/s. Note: the elocity readout will not work until you hit the Collect button. The elocity will slow down as soon as you stop spinning it, DO NOT try to keep it going during an experiment, a changing elocity is what we want for this experiment. 4. DO NOT place any part of your body in the path of the arm, you will hurt yourself and ruin you calibration of the setup. If you need to stop the arm gently grab the same section of rod you used to spin the arm and use it to slow the arm. 5. Hit the Collect button. 6. Note: Logger Pro defaults any elocity as een though we are measuring angular elocity w. It will not affect the results, just keep it in mind. 7. Plot F s. w 2 and from this graph determine a alue for M using the radius you measured earlier. Watch your units. 8. Compare this experimental alue for M exp to the measured alue for M th. 9. Perform identical experiments (as many as time allows) to confirm your results. Perform any statistical calculations you think are necessary. I am purposely leaing this step up to you, time for you to impress your instructor with all that you hae learned! 10. Repeat Steps 5-9 for 2 additional mass alues. Centripetal Force - 7

8 Questions 1. What is the benefit of plotting F s. w 2 as opposed to F s. w? Does changing an axis change the data or the end results? 2. How well does your experimental alues match up with the theoretical alues? 3. How does the statistical analysis affect your confidence in your final result? 4. What are some of the possible sources of error associated with the apparatus and/or measurement technique? (Note: Human error is not an acceptable answer, think about fluctuations in measurements and their result on the final answer.) Centripetal Force - 8