Laboratory Investigation Abstract: Analysis of the circular motion of a swinging stopper will provide insight into the causes of centripetal force and develop relationships between speed, radius and centripetal force. Name: M1
Procedure: 1. Measure the mass of the rubber stopper using a scale and record in the attached data table. 2. Attach 200 g of mass to the bottom of the string that passes through the tube. Refer to the diagram to understand how to measure the radius. Before swinging the stopper, measure the radius so that it will be somewhere between 50 60 cm and record this value. RADIUS USED: 3. Put an alligator clip on the string just underneath the bottom of the tube and wrap the string once around one side of the clip teeth so that the clip will not slide if pushed (see diagram). PART 1 Changing Mass READ UP TO STEP 5, BEFORE BEGINNING Practice swinging Hold the apparatus as shown in the picture and use your free hand to hold the weight hanging below the tube. Begin swinging in short horizontal circles to make the stopper go in a horizontal circle around your head. Once you get it moving, slowly release the weight in your hand until it hangs freely. Place alligator clip ary the speed at which you swing the stopper until you can get the alligator clip to be just below the bottom of the tube without it touching the tube. Keep the swing constant so that the alligator clip remains in place and does not move up or down. 4. In this part of the lab we will be varying the mass hanging on the rope. Choose a starting mass of either 100 or 200 grams. If you are able to swing the mass successfully with the 100 gram weight, then start with that mass, however, if the stopper is too heavy and it is difficult to swing with such a small weight then start with the 200 gram mass. 5. We will now take data while spinning the stopper, please read the recommendations that follow, don t be lazy. Sometimes the stopper will be swinging quickly so be careful when you are counting the revolutions. The person swinging the stopper usually has the best idea about the numbers of revolutions and you can even hear the swirling noise of the stopper to help you count. The person doing the swinging can begin counting aloud from 1 27, and the person timing can start the stopwatch when they hear 5, and then stop at 25 so there will be a more accurate result of the beginning and end of the 20 revolutions. Use whatever method is best for your lab group for counting and timing. Record your data in the attached data table. Make sure the stopper is spinning at a constant rate in a horizontal circle and the alligator clip remains at the same spot (just below the tube but not touching), and record the amount of time required to make 20 revolutions of the stopper. 6. Repeat step 5 one more time so that you will have two trials total. 7. Add an additional 100 g of mass hanging to string to increase the total mass Repeat the two swing trials again and record your times on the data table. 8. Add another 100 g of mass (200 g total additional added) Repeat the two swing trials again and record your times on the data table. 9. Add a final additional 100g of mass (300 g total additional added) Repeat the two swing trials again and record your times on the data table. M2
PART 2 Changing Radius 1. Copy the data from the first row of part 1 table and make an exact copy in the first row of part 2 data table. 2. For rows 2 4 in the part 2 table, use the initial amount of hanging mass on the string as you did in part 1, and do not add or remove mass for any part. In this part of the lab we will vary the radius at which the stopper spins around. 3. Move the alligator clip 10 cm up or down the rope from its current location (this will make a different radius when the string is swung). Again wrap the string around one of the alligator teeth so that it will not slide if pushed. Record the value of the new radius in your table. 4. Repeat the experiment as conducted before so that the clip is just barely below the glass tube and does not move. Get the time to make 20 revolutions. Repeat this step 1 more times for a total of 2 trials. 3. Move the alligator clip to another different location (10 cm different than other trials) and record it. Measure and record the time for 20 revolutions. Repeat this step 1 more time for a total of 2 trials. 4. Again, move the alligator to a new location (10 cm different from other trials) and record the time for 20 revolutions. Repeat this step 1 more time for a total of 2 trials. END OF EXPERIMENT M3
Analysis Instructions A common mistake in this lab is misunderstanding which mass to use. There are two masses, the hanging mass (the one hanging below the circle attached to the string) and the mass of the stopper. Each mass is used for a different thing in the analysis. Keep in mind that the stopper is the thing that is going in the circle, so when using circular motion analysis it is the stopper mass that is being accelerated. Complete the calculations on the data worksheet. Read the directions below to assist you. (a) mass weight and Fc Why does the spinning stopper maintain its circular motion in this lab? The stopper goes in a circle because a centripetal force allows it to happen. A centripetal force is always provided by something. In this case the string tension provides the centripetal force. However, if there was no mass attached to the string then the stopper would just fly away and the hanging mass creates the tension which provides the centripetal force, so in essence the weight of the hanging mass provides the centripetal force acting on the stopper. (note, if you are one of the few people that actually read directions, this paragraph is the basis for the answer to one of the questions, congratulations.) This important relationship directly gives us F c. Now that we know the F c we can calculate other values. (b) Speed () We are going to find the speed of the stopper with two methods and compare the results. For the purposes of percent error, we will assume that Method 1 is the experimental value and Method 2 is the actual value. Method 1 (experimental ) find the speed using distance and time. In lab we found the time needed for 20 revolutions which we can easily use to find the Period. (Period =time needed to make 1 revolution) We also know the distance traveled in 1 revolution. The stopper swings in a circular path and we know the radius of this circle. The distance traveled in 1 revolution around a circle is the circles circumference C = 2 π r With the distance and time traveled, we can find the speed of the stopper in the circle. This is method 1. Method 2 (actual ) find speed using the known centripetal force In accordance with the discussion in part (a) of this analysis we know the centripetal force on the stopper. We also know the mass of the stopper and radius of the swing. Given the formula for centripetal force: F net(c) = m a c F net(c) = mv r We can see that the only unknown left in the equation is v so we can rearrange the equation to solve for v. Read the note at the top of this page again to be sure to use the correct values. (c) Find the percent error for the two methods of v Graphs Attach 2 1. Make a graph of centripetal force vs. speed(method 1) for part 1 of the lab ( y vs. x ) 2. Make a graph of speed(method 1) vs. radius for part 2 of the lab ( y vs. x ) M4
Centripetal Force Lab Name: When turning in the lab, only turn in from this page forward. The prior pages are for your reference only Data and Calculations Table Part 1 Constant Radius, Changing Mass ALL MASSES SHOULD BE CONERTED TO kg shaded columns = data to record during lab Mass (kg) Weight of mass (N) Radius (m) Mass of Stopper (kg) for 20 revs (s) Trial 1 Trial 2 for 20 revs (s) Average for 1 rev (s) F c (N) Method 1 Method 2 % error Sample Calculations: Part 2 Constant Mass, Changing Radius Mass (kg) Weight of mass (N) Radius (m) Mass of Stopper (kg) for 20 revs (s) Trial 1 Trial 2 for 20 revs (s) Average for 1 rev (s) F c (N) Method 1 Method 2 % error
Questions 1.) List reasons for error in any part of this experiment. Do Not simply write human error or miscalculations or rounding ; those are not reasons for error. Reasons for error can include human factors, but you should specifically state what they are rather than writing human error. Furthermore, errors are not mistakes or things you could correct, rather they are uncontrollable and could be there no matter how many times the experiment is conducted. 2.) Explain how you found the F c acting on the stopper and why this is the correct way of calculating it. 3.) What does graph 1 suggest about the relationship between speed and centripetal force? Does this make sense, explain? (you must refer to a physics formula) 4.) What does graph 2 suggest about the relationship between speed and radius? Does this make sense, explain? (you must refer to a physics formula) 5.) Which method of solving for v do you think is more accurate and why (Don t refer to one formula being harder than the other, accuracy should be based on the values used to find answer, not the actual formulas themselves) M6