CENTRIPETAL FORCE ON A PENDULUM

CENTRIPETAL FORCE ON A PENDULUM
OBJECTIVE
To measure centripetal force exerted on a pendulum using the force sensor bob and in so doing compare this value determined by force calculations based on the height of the pendulum.
THEORY
Newton’s laws of motion are the basis for this experiment. Newton’s first law of motion states that a body in motion will remain in motion unless acted upon by an external force. Newton’s second law of motion states that the rate of momentum of a body is dependent on the product of its mass and acceleration. Where rate of change of momentum is given by =
A pendulum bob follows a circular path and is therefore acted upon by centripetal force. In this experiment the tension in the string causes the bob to follow a circular path. From Newton’s second law of motion above it is related to the experiment as shown = T- mg =ma =
Where T is the tension in the string m is the mass of the pendulum g is acceleration due to gravity is the centripetal force
The force measured by the force sensor when the pendulum passes through the lowest point of the swing is equal to centripetal force. This is because the force sensor is zeroed when the pendulum is at rest in its equilibrium position, where T= mg.
Centripetal force can also be found from the relationship below using the speed, v, when the bob passes through the lowest point =
Where
r is the radius of the circular path (for the experiment it is equal to the length of the pendulum) It can also be found from the relationship of the height of the bob at the top of the swing =
Where h is the maximum height of the bob g is the acceleration due to gravity APPARATUS
Passport force sensor
Passport USB link
Computer equipped with Data Studio software
Horizontal rod
Support stand
100 gram mass
Thread
Ruler
Procedure
The centripetal force of the pendulum bob at its lowest point is determined here using the force sensor.
1. The tab “Exp 8- DataStudio” in the Moodle course shell was clicked and the file with DataStudio Executable option opened.
2. The activity was then saved on the computers desktop for easy retrieval after the DataStudio file opened.
3. The force sensor was plugged into the USB link interface and the interface plugged into a USB port on the computer.
4. The interface was plugged into the computer and the plug and play sound was heard.
The force sensor was used to measure centripetal force on a pendulum bob at the lowest point of its swing. The photogate was used to measure the time the pendulum bob blocks the photogate beam. The value of the diameter of the pendulum bob was entered. DataStudio calculated and displayed the speed of the pendulum bob and he centripetal force on the pendulum for the bottom of the pendulum swing.
5. The force sensor was mounted on a horizontal rod with the hook end down.
6. The other end of the horizontal rod was mounted lower down on the support stand.
7. A piece of thread about 30 cm long was used to make the pendulum. One end of the string was tied to the hook on the force sensor and the other end tied to the 100 gram mass.
8. The right angle clamp was loosened and the horizontal rod, raised with the force sensor up until the mass was lifted above the base plate of the support stand.
9. The length of the pendulum was measured from the bottom of the force sensor’s hook to the middle of the pendulum bob. The length of the pendulum bob was recorded in the data table below.
10. The distance from the bottom of the bob to the table top was measured.
11. The release height the pendulum was determined from where the pendulum bob needs to be released from by added six centimetres to the bob starting height and this height was recorded in the data table.
The pendulum bob was pulled back and using a ruler the pendulum was released from the height. The centre of the bottom of the bob was at this height.
The pendulum bob was swung in the direction of the sensor hook fork.
Data Recording
1. The tare button was pressed to zero the force sensor when the pendulum bob is at rest.
2. The pendulum was set in motion and allowed to swing back and forth for a while.
3. The data was recorded as the experiment was conducted.
DATA ANALYSIS