Experiment P30: Centripetal Force on a Pendulum (Force Sensor, Photogate)

Transcription

1 PASCO scientific Physics Lab Manual: P30-1 Experiment P30: (Force Sensor, Photogate) Concept Time SW Interface Macintosh File Windows File centripetal force 30 m 500 or 700 P30 Centripetal Force P30_CENT.SWS EQUIPMENT NEEDED Interface horizontal rod ±50 Newton force sensor mass set (for calibration) photogate pendulum (e.g., metal cylinder) balance right angle clamp base and support rod string calipers PURPOSE The purpose of this laboratory activity is to measure the centripetal force exerted on a pendulum bob directly using the force sensor and to compare the measured force to the calculated force based on the speed of the pendulum. THEORY A pendulum bob follows a circular path. Therefore, it is acted on by a centripetal ( center-seeking ) force. In the case of the pendulum, the tension in the string causes the bob to follow the circular path. At the bottom of the pendulum s swing the net force on the bob is the combination of the tension in the string and the force of gravity. m = mass T = tension mg = weight According to Newton s Second Law, ΣF = T mg = ma = F c where T is the tension in the string, m is the mass of the pendulum bob, g is the acceleration due to gravity, and Fc is the centripetal force. The force sensor will be zeroed when the pendulum is at rest in its equilibrium position (or T = mg). Thus the force measured by the force sensor when the pendulum is in motion is equal to the centripetal force Fc as the pendulum bob passes through the lowest point of the swing. The centripetal force can also be found using the speed, v, of the bob as it passes through the lowest point of the swing using: F c = m v2 r where r is the radius of the circular path which, in this case, is equal to the length of the pendulum. PROCEDURE For this activity, the force sensor measures the centripetal force on a pendulum bob as it swings back-and-forth. The photogate measures the time that the pendulum bob blocks the photogate beam. You will enter the value for the diameter of the pendulum bob. The jhn 1996, PASCO scientific P30-1

2 P30-2: Physics Lab Manual PASCO scientific program calculates and displays the speed of the pendulum bob and the centripetal force on the pendulum. You can use the program to calculate centripetal force based on the measured speed of the pendulum bob. The calculated and measured values of centripetal force will be compared. PART I: Computer Setup 1. Connect the interface to the computer, turn on the interface, and turn on the computer. 2. Connect the force sensor's DIN plug into Analog Channel A on the interface. Connect the photogate s stereo phone plug into Digital Channel 1 on the interface. 3. Open the document titled as shown: Macintosh P30 Centripetal Force Windows P30_CENT.SWS The document will open with a Graph display of Force (Newtons) and Velocity (m/sec). Note: For quick reference, see the Experiment Notes window. To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. Change the Experiment Setup window by clicking on the Zoom box or the Restore or Maximize button in the upper right hand corner of that window. 4. The Sampling Options are as follows: Periodic Samples = Fast at 100 Hz (one hundred samples per second) and Start Condition = Channel 1, Low (recording begins when the photogate connected to Digital Channel 1 is first blocked). P , PASCO scientific jhn

3 PASCO scientific Physics Lab Manual: P30-3 PART II: Sensor Calibration and Equipment Setup Sensor Calibration 1. To calibrate the force sensor, change the Experiment Setup window to full size by clicking on the Zoom box or the Maximize button in the upper right hand corner of that window. Full size Zoom box Restore button Minimize button Close box Control-menu button Maximize button Macintosh Reduced size Windows 2. In the Experiment Setup window, double-click the force sensor s icon to open the Force Sensor setup window. The Force Sensor setup window shows the default calibration values (i.e., a push of 50 Newtons produces 8 Volts; a pull of -50 Newtons produces -8 Volts). The force sensor is set up so that a pull away from the sensor is a negative force. For example, if a one kilogram object is hung vertically from the hook, the force sensor measures -9.8 Newtons (since the force is downward). 3. Mount the force sensor on a horizontal rod with the hook pointing down. Do not put an object on the sensor s hook yet. jhn 1996, PASCO scientific P30-3

4 P30-4: Physics Lab Manual PASCO scientific 4. For the High Value calibration point, press the tare button on the side of the force sensor to zero the sensor. Click the Read button for High Value. Since there is no object on the sensor s hook, type 0 as the High Value. 5. For the Low Value calibration, hang an object of known mass on the sensor s hook. 6. Click the Read button for Low Value. Enter the object s weight in Newtons (mass in kilogram x 9.8 N/kg). Remember, enter the object s weight as a negative value (a force pulling away from the sensor). Force Sensor Object of known mass In this example, the object has a mass of grams ( kg), or a weight of Newtons (entered as ). 7. Change the force sensor Sensitivity. Click the Sensitivity Menu button. Change from Low (1x) to Med (10x). 8. Click OK to return to the Experiment Setup window. P , PASCO scientific jhn

5 PASCO scientific Physics Lab Manual: P You do not need to calibrate the photogate. However, you do need to enter the value of the diameter of the pendulum bob into the program. 10. Measure the diameter of the pendulum bob. Record the diameter. 11. In the Experiment Setup window, double-click the photogate s icon to open the Photogate Setup window. diameter of pendulum, d = m 12. Change the default value of the Object Length (0.100 m) to the value of the diameter of the pendulum bob. (The diameter is m in the example.) 13. Click OK to return to the Experiment Setup window. Equipment Setup 1. Mount the force sensor on a horizontal rod with the hook end down. 2. Measure the mass of the pendulum bob. Record the mass in the Data section. mass of pendulum, m = kg jhn 1996, PASCO scientific P30-5

6 P30-6: Physics Lab Manual PASCO scientific 3. To make the pendulum, use a piece of string that is about one meter long. Tie one end of the string to the hook on the force sensor and tie the other end to the pendulum bob. 4. Arrange the photogate so the pendulum bob blocks the photogate s beam when the bob is at rest. The center of mass of the pendulum bob should be approximately at the same height as the photogate beam. 5. Measure the length of the pendulum from the force sensor s hook to the center of the pendulum bob. String Force Sensor length, r = m Pendulum Photogate NOTE: Not to scale. Preparing to Record Data When all the equipment is ready, practice swinging the pendulum bob. Pull the pendulum bob to the side about 15 to 20 centimeters. Gently release the bob so it swings through the photogate as smoothly as possible. Adjust the position of the photogate if necessary. PART III: Data Recording NOTE: Don t let the pendulum bob hit the photogate! 1. While the pendulum bob is at rest, zero the force sensor by pressing the tare button on the side of the force sensor. 2. Set the pendulum in motion. Let the pendulum swing back-and-forth several times to allow any oscillations to dampen out. P , PASCO scientific jhn

7 PASCO scientific Physics Lab Manual: P Click the REC button ( ) to begin. 4. Record data for about 20 seconds. Click the STOP button to end data recording. Run #1 will appear in the Data list in the Experiment Setup window. ANALYZING THE DATA 1. Click the Graph to make it active. Click the Autoscale button ( ) to rescale the graph to fit the data. The Graph will display a plot of the pendulum s velocity and a plot of the pendulum s centripetal force. The plot of speed should be linear. The plot of centripetal force should be sinusoidal. 2. Click the Smart Cursor button ( ). The cursor changes to a cross-hair shape when you move it into the Graph display. The X- and Y- coordinates of the position of the cursor are displayed next to the horizontal and vertical axes of the Graph. 3. Move the cursor/cross-hair to the first or second peak on the plot of centripetal force. The Y-coordinate at that point is the maximum centripetal force on the pendulum. Record the value of centripetal force in the Data section. (Fc = Newtons in the example.) jhn 1996, PASCO scientific P30-7

8 P30-8: Physics Lab Manual PASCO scientific 4. Press and hold the SHIFT key on the keyboard. This will freeze the horizontal position of the Smart Cursor. Move the cursor vertically into the plot of velocity and place the cursor at the point that corresponds to the peak you measured in the plot of centripetal force. The Y- coordinate at that point is the maximum speed of the pendulum. Record the value of speed in the Data section. (v = m/sec in the example.) 5. Repeat the data analysis process for four more peaks on the plot of centripetal force. Record the maximum centripetal force and the corresponding speed in the Data section. 6. For each value of speed you measured, calculate the centripetal force using the mass, speed, and length (r) of the pendulum. Record the calculated value of centripetal force in the Data section. 7. Calculate the percent difference between the measured centripetal force and the calculated centripetal force for each point you measured. Record the difference in the Data section. DATA TABLE mass, m = kg length, r = m No. Fc, measured (N) v (m/sec) Fc, calculated (N) % difference QUESTIONS 1. How do your measured valued of centripetal force compare to the calculated values of centripetal force? 2. What are possible reasons for the differences between the measured and calculated values of centripetal force? P , PASCO scientific jhn