Procedures: A. Experiment 1: Varying Mass 1. 1D. 11. Attach a 20-g{.020-kg} mass to the side of the armature with the wire attached to the screw. To do this unscrew the plastic nut from the screw; place one mass so the screw is In the hole and secure the mass by screwing the nut back onto the screw above the mass. Make sure that the mass ls able to slide freely In the slot. Adjust the thumbscrew and hardware If necessary. Move the force sensor rod up or down so the center of the freely sliding 20-g mass has a radius of 5cm [0.050m}. To determine the radius of the mass; gently pull the mass towards the end of the armature so the wire is taught. Where the screw stops ls where the mass will end up once the arm ls rotating. This means that you want to hold the screw on that mass at the 5cm mark, and adjust the height of the force sensor accordingly. Record the total mass ofa zg [BASED-kg} mass plus all the hardware that Is used to attach an object to the rotating arm of the centripetal force apparatus on the data sheet below. Hardware weighs 3.0-g per side Including the thumb screw. To balance the rotating army attach another 211g mass on the other side of the platform as a counterweight. Position this non-sliding ZD-g mass so Its center Is also 5cm from the center of the rotating arm. Press the zero button on the force sensor. Click the "on" button in the signal generator. Slowly Increase the voltage In the signal generator until It reads Sr'v'olts output by clicking on the up arrow next to the voltage offset. Once you have reached E-Volts, close the signal generator and click the record button. Allow the armature to run for 23 seconds before stopping the data acquisition by clicking the record button again [it should have changed to a stop button}. Then slowly lower the voltage back to zero. Record all data necessary In the table labelled Ivarying Mass on the data sheet. i. 0n the graph; click the I 7 button to find the average force. This Is the "Measured Force\" in the table. il. Record the "BIocktoBlock Time\"' as the period In the table. iil. Use Equations :3} and [T] to determine the calculated force. iv. Determine the percent difference between the calculated force and the measured force. Report this In the "9r. Error' table on the data sheet. Once the armature Is not moving, add an additional 1&g {Ulllkgl mass to the freely sliding mass and the stationary mass. Measure and record the mass on the data sheet, and repeat the data recording procedure [steps 5 through 9}. Remember, record the total mass of the obiect per side [the mass plus the hardware}. For the third and fourth runs, repeat the process for d-Og per side; then for 50g per side. Make sure you keep track of which set of masses was used for each run. B. Experiment 2.- Ivarying Radius 1. With the armature not moving, use the thumbscrevuI and other hardware on the apparatus to attach Sag {UBSCFkg} worth of mass to the wire end of the rotating arm. Make sure that the mass is able to slide freely in the slot. Adjust the thumbscremiI and hardware if necessary. 2. Move the force sensor rod up or down so the center of the freely sliding SDg of mass has a radius of 5-cm {USDm} insert the radius on the data sheet. 3. To balance the rotating arm, attach another SDg of mass on the other sIde of the platform as a counterweight. Position thIs nonsliding Sgof mass so its center is also S-cm from the center of the rotating arm. Press the zero button on the force sensor. Click the "on\" button in the signal generator. 6. Slowly Increase the voltage In the signal generator untIl It reads iii-Volts output by clicking on the up arrow next to the voltage offset. T. Once vou have reached B-Volts, close the signal generator and click the record button. Allow the armature to run for 2-3 seconds before stopping the data acquisition by clicking the record button again lit should have changed to a stop button}. then slowly lower the voltage back to zero. 8. Record all data necessary In the table labelled IIi'arvlng Radius on the data sheet below. '.-"':""' I. Dn the graph. click the I V button to find the average force. This Is the "Measured Force\" in the table. ii. Record the "BIocIttoBioclt Time\"' as the period In the table. iiI. Use Equations [3] and [T] to determine the calculated force. iv. Determine the percent difference between the calculated force and the measured force. Report this In the "it. Error' table on the data sheet. 9. With the armature not moving, adjust the position of the SID-g of mass on the rotating arm so that the center of each set Is at a radius of E-crn [MED-ml, and enter the radius on the data sheet. 10. Repeat steps 4 9 above with two more positions for the masses: S-cm {0.080-m] and 10{m{0.1-m} radli. C. Exgerimenta: 'v'arying Speed 1. E" 10. Analysis: With the armature not moving, use the thumbscrew and other hardware on the apparatus to attach SDg [(1050-ng of mass to the wire and the rotating arm. Make sure that the mass is able to slide freely in the slot. Adjust the thumbscrew and hardware if necessary. Move the force sensor rod up or down so the center of the freely sliding mass SDIg of mass has a radius of 5cm (HOBOml. To balance the rotating arm, attach another SDg of mass on the other side of the platform as a counterweight. Position this nonsliding SCIg of mass on the other side of the platform as a counterweight. Position this nonsliding SDg of mass so its center is also Scm from the center of the rotating arm. Press the zero button on the force sensor. Click the "on" button in the signal generator. Slowly increase the voltage in the signal generator until it reads 4-Volts output by clicking on the up arrow next to the voltage offset. Once you have reached 4-'v'olts, close the signal generator and click the record button. Allow the armature to run for 23 seconds before stopping the data acquisition by clicking the record button again {it should have changed to a stop button}. Then slowly lower the voltage back to zero. Record all data necessary in the table labelled Varying Speed on the data sheet below. i. (In the graph, click the I ' button to find the average force. This is the "Measured Force" in the table. ii. Record the "Block-to-Block Time" as the period in the table. iii. Use Equations [3] and {7'} to determine the calculated force. iv. Determine the percent difference between the calculated force and the measured force. Report this in the "96 Error" table on the data sheet. For the second run, keep the mass and radius constant. Repeat steps 4-8 above, this time increasing the voltage from CW to 6V. Repeat three more times with final voltages of 8V, 10V, and 12V. Make sure you record the blocktoblock time for each run, and keep track of which run corresponds with each speed. 1. Print and label one representative graph from each of your three experiments to turn in with your lab report. 2. For each of your three experiments, use your favorite graphing program to plot force vs the variable in question for both the calculated and measured values. Centripetal Force - Data Sheet Physics 231 Name: Date: 6/7/2023 Varying Mass: Run # Mass Radius Period Calculated Force Measured Force 1 0.023 kg 0.05m 13 s 2.69 N -2.7 N 2 0.033kg 0.05m 13 s 3.87 N 3.8 N 3 0.043kg 0.05m 13 s 5.04 N 4.8 N 0.063kg 0.05m .13 s 7.38 N -6.8 N Varying Radius: Run # Mass Radius Period Calculated Force Measured Force 1 0.53 kg 0.05 m .13 s 6.21 N -6.1 N 2 0.53 kg 0.06 m .13 s 7.43 N 7.0 N 3 0.53 kg 0.08 m . 13 s 9.91 N -8.7 N 4 0.53 kg 0.1 m .13 s 12.35 N -11.0 N Varying Speed: Run # Mass Radius Period Calculated Force Measured Force 1 0.53 kg 0.05 m 28 s .33 N -1.0 N 2 0.53 kg 0.05 m 18 s 3.21 N 2.5 N 3 0.53 kg 0.05 m 13 s 6.21 N -5.3 N 4 0.53 kg 0.05 m 10 s 10.45 N -12.1 N 5 0.53 kg 0.05 m 0.08s 16.37 N -15.9 N % Difference Calculations: Varying Mass Varying Radius Varying Speed 37% 1.77% 24.8% 1.87% 5.79% 4.76% 12.2% 14.65% 7.86% 11.0% 15.79% X X 2.87%Centripetal Force Physics 231 At the end of the lab experiment please clean your table and wait for the instructor to check you out. All of the group partners must be present. Thank you. Note: This document has been adapted from material freely available from the Pasco website. Pasco and Capstone are trademarks of Pasco, Inc. Equipment: centripetal force apparatus 20-g circle masses (6 per group) 10-g circle masses (2 per group) 5-g circle masses (2 per group) 850-UI Introduction: In this lab, you will be investigating the effects of varying three different quantities on centripetal force: The amount of mass that is being rotated, the radius at which the mass is rotating and the speed at which the mass is rotating. Background: A. Circular Motion Circular motion describes motion in (unsurprisingly) a circle. The circumference (distance around the circle) of a circle is given by the equation Circumference = 2nR (1) where R = radius of the circle The speed of any object is (distance traveled) (time to go that distance) -(2) For objects moving in uniform circular motion (i.e. motion in a circle at constant speed), the speed can be found by dividing the circumference of the circle by the period, or period of revolution, which are both names for the time the object takes to go around the circle once: V= =(3) where V - speed R o radius To periodCentripetal Acceleration Centripetal acceleration is acceleration towards the center of a circle (the word "centripetal" means "acting towards the center"). Recall that acceleration is given by AVeloc Ty(4 Atime and that velocity has both a direction and a magnitude (the magnitude of velocity = speed). If either the direction or speed of an object changes, then it experiences an acceleration. For an object moving in a circle at constant speed, the direction of motion changes constantly. Therefore, it experiences an acceleration. The formula for centripetal acceleration is Acentripetal - -(5) where v = speed R - radius of the circle Note that because the object is always moving with respect to the center of the circle, the direction of the centripetal acceleration vector is also always changing. C. Centripetal Force By Newton's Second Law, we know that Force = Mass X Acceleration (6) For an object of Mass = m that is experiencing centripetal acceleration, we find that the equation for centripetal force is Fcentripetal =(7) where m = mass vo speed R o radius This is the force that acts on an object to keep it moving in a circle and the source of this force depends on the physical situation. For a satellite in circular orbit around the earth, gravity provides the centripetal force. For a car negotiating a turn in the road, friction provides the centripetal force. Like the centripetal acceleration vector, the centripetal force vector also constantly changes its direction.D. Special note on the difference between "centripetal" and "centrifugal" The word "centripetal" means "center-acting", or a force that acts towards the center of a circle. This is the proper term for any force that keeps an object moving in a circle. The word "centrifugal" is commonly used by non-scientist to mean what we would call centripetal. The work "centrifugal" means "center-fleeing", or a force that acts away from the center of the circle. There are two basic cases when the word "centrifugal" properly applies. In the first case, imagine a bug at the bottom of a can. A child whirls the can in a circle overhead. The tension in the string exerts a centripetal force, as does the force of the can on the bug. However, the Newton's Third Law pair reaction force (the force of the bug on the bottom of the can) acts away from the center of the circle and is therefore a centrifugal force. The second situation, the details of which will not be given here, concern a supposed "fictitious force" that arises when an object is placed in a rotating reference frame. Setup: Follow these instructions for setting up the equipment for the lab. 1. The experimental apparatus should already be partially set up and look similar to the photo below: Pasco Force Sensor Rotating Arm A Weights Photogate2. Make sure that the base of the experimental apparatus is balanced (using the screws on the feet of the base and a bubble level from the front of the lab.) 3. Connect the Pasco force sensor to the PasPort 1 port on the 850-UI with the silvery cord. 4. Connect the motor at the base of the apparatus to the function generator ports on the 850-UI. Plug the red banana plug wire into the red port and the black banana plug wire into the black port. 5. Connect the photogate head on the centripetal force apparatus to the digital input 1 on the 850-UI using the black *" cord. Ensure that the cord is out of the way of the rotating arm. 6. The front of the 850-UI should look like this when all are plugged into it: 0090 O 7. Turn on the 850-UI and open the Capstone software. If the 850-UI is not turned on before opening the software, the software may not work correctly. 8. Click on the hardware setup in the column on the left. a. Click on the PasPort 1 port on the diagram and select "force sensor" if the sensor does not already show on the diagram (looks like this b. Click the digital input 1 on the diagram and select "photogate with pulley" if the photogate does not already show on the diagram.IF HINT 9. Click on timer setup in the left column. a. Numbers one, two and three should be fixed and unable to be changed. b. Make sure in number 4 that "Block-to Block Times" is checked. This is the only measurement we will be using, so feel free to uncheck the others if you wish. C. Number five should have 0.015 for Spoke Arc Length and 36 for Spoke Angle. . ""Make sure you hit SAVE at the bottom of the timer setup." " If you do not, you will not find Blobk-to Block times as a variable option. 10. Click on signal generator in the left column. a. Under 850 Output 1 select DC for the waveform. b. The only thing you should need to change during your procedures is dicking the on and off button and dicking the up and down arrows next to the box for "DC Voltage". C. Lower the DC Voltage to O and click "On". During your procedure, you will use the voltage to increase and decrease the rate of rotation for your amature. d. To stop the rotation of the amature, click the down arrows to return to zero, or click "off" in this screen if you need to stop the armature immediately. e. Click on Signal Generator again to close the window. 11. Double click on the "table and graph' template. Set the y axis of the graph to Force. Set one of the columns in the table to "Block to Block Times"- 12. You should now be ready to take data