Title : Centripetal Force on a Pendulum
Apparatus :
Science Workshop Interface 750 1
Force sensor ( PASCO CI-6537 ) 1
Photogate ( PASCO ME-9204B ) 1
pendulum bob 1
- cylindrical in shape
- radius about 3.2 cm
stand - and - clamp 1
string 1
triple beam balance 1
vernier caliper 1
metre rule 1
Objective :
1. Measure the centripetal acceleration of the bob by using the photogate
when a pendulum bob reaches the lowest position
2. Measure the centripetal force by using a force sensor
3. Study the difference between measured centripetal force and
calculated centripetal force
Theory :
The Photogate Head emits an infrared beam from one side of it's "U" shape to the other. Timing begins when an object interrupts the infrared beam. A light-emitting diode (LED) on the top of the Photogate Head shows when an object blocks the beam.
The Force Sensor measures between + 50 and - 50 newtons. The sensor output is + 8 volts for a force of + 50 newtons and - 8 volts for a force of - 50 newtons. Pushing on the sensor's detectable hook produces a positive voltage and pulling produces a negative voltage.
A pendulum bob follows a circular path. In the case of the pendulum, the tension,T , in the string causes the bob to follow the circular path. At the bottom of the pendulum's swing the net force is the combination of the tension, T, in the string and the force, mg, due to gravity.
and 
The Force Sensor will be zeroed when the pendulum is at rest in its equilibrium position. Thus the force measured by the Force Sensor when the pendulum passes through the lowest point of the swing is equal to the centripetal force.
The centripetal force always points towards the point of support which is the centre of the arc length. In particular, at the lowest position, the centripetal force is vertically upwards.
Procedure :
Hardware setup :
1. Connect the Interface to the Computer, turn on the interface, and turn on the computer.
2. Connect the Force Sensor and Photogate to the interface
3. Use the Force Sensor to measure the tension of the string and the Photogate to measure the
velocity of the bob
4. Use a vernier caliper to measure the diameter of the pendulum bob and triple beam balance to
measure the mass of the pendulum bob.
5. Tie one one of one metre long string to the hook on the Force Sensor and tie the other end to
the pendulum bob.
6. Arrange the Photogate so the pendulum bob blocks the Photogate's beam when the bob is at
rest.
7. When the pendulum bob is at rest, zero the force sensor by pressing the "tare" button. Use a
Digital display to monitor the force sensor reading. The reading of the force sensor is the
centripetal force.
Without zero setting at the equilibrium position, the centripetal force is
the force sensor reading - m g.
8. Pull the pendulum bob to the side about 15 cm. Gently release the bob.
Do not let the pendulum bob hit the Photogate.
Software setup :
Force Sensor Calibration
Click - and - drag the 'analog sensor plug' icon to the Channel A icon in the Experimental Setup window, select the name of the sensor from the list of sensors and click 'OK' to return to the Experiment Setup window.
In the Experiment Setup window, double - click the force sensor's icon.
Calibrate the software :
1. DO NOT apply a force to the sensor. Press the 'tare' button to zero the sensor.
2. Check the voltage under next to 'Cur Value'. When the voltage stabilizes, click the 'Read'
button in the row for 'Low Value'. Enter '0' as the force value.
3. Use object of known mass to apply a pulling force on the hook. When the voltage
stabilizes, click the 'Read' button in the row for 'High Value'. Enter the force value. For
example, enter '9.8' for a one kilogram mass.
4. The Force Sensor sensitivity should be set at Medium ( 10X ). If the pendulum bob is more
than 0.5 kg, change the sensitivity to Low ( 1X ).
5. Click 'OK' to return to the Experiment Setup window.
Photogate software setup :
Click - and - drag the 'digital sensor plug' icon to the Channel 1 icon in the Experiment Setup window, select 'Photogate & Solid Object' from the list of sensors and click 'OK'. Enter the diameter of the 'Object' and click 'OK' to return to the Experiment Setup window.
Set up a display
Click - and - drag the 'Graph' display icon to the sensor's icon in the Experiment Setup window to open the Graph display to show both Force - time and Velocity - time graphs.
Data Recording :
1. Press the Sampling Option button to open a window.
2. Select the Periodic Samples to 2000 Hz and the Stop Condition to 10 seconds.
3. Click the Record (REC) button to begin recording data.
Data sampling would stop automatically.
Data Analysis :
Compare the measured maximum centripetal force and the calculated value of the centripetal force using the mass, speed, and length of the pendulum.
Discussion :
1. What are the factors that affect the centripetal force on a pendulum
as the pendulum swings back and forth ?
2. What are possible reasons for the differences between the
measured and calculated values of centripetal force ?
3. Discuss the application of centripetal force in our daily life.
( one example )