ABSTRACT
The pendulum lab was performed to experiment the dependence of period on the acceleration due to gravity. As the angle of the plane increases, the acceleration due to gravity decreases. The period of the pendulum increases as the angle of the plane increases. When the angle of the plane is titled, it reduces the
acceleration due to gravity because the restoring force is decreased. The
acceleration is varied by tilting the plane of pendulum by angle θ from
vertical. The component of gravity that affects the motion of the period is g
cos θ since the g sin θ cancels with the tension force acting on the rod.
Procedure
Setup
Procedure
- Mount the rotary motion sensor on the rod stand
- Attach the angle indicator and put the pulley on the motion sensor.
- Attach the rod and add a 150 gram mass on the pulley.
- Plug the motion sensor into a Pasport input on the 850 Universal Interfac
Procedure
- Displace the pendulum about 10 degrees from equilibrium at 0 degrees plane.
- Click record and let the timer run for about 20 seconds.
- Repeat the step by increasing 5 degrees of the plane every time and record the amount of time it takes for the pendulum to complete one oscillation.
- Continue until the angle 85 degrees.
Equipment
- Rod clamp
- Rotary motion sensor
- Aluminum rod 175 g
- Angle Indicator
- Two 75 g masses
- Computer
- Rod Stand
- PasPort input
Observations
MEASUREMENT:
- Length of the rod = 35.7 cm
- Length of the rod with two masses = 33.3 cm
- Length of the rod with one mass = 35 cm
- Mass of the rod = 26.5g
analysis & discussion
T=2πLg‾‾√cosx
In this formula, L is the length of the string and g is the acceleration due to gravity (about 9.8 m/s^2) and x is the angle of the pendulum. From this equation, it can be seen that only factor that affect the period of a simple pendulum are its length, the acceleration due to gravity and the angle of the pendulum. The period is completely independent of other factors, such as mass.
It was seen in the experiment that the measured value of time period was almost similar to the theoretical value of the time period up to the 60° angle of the pendulum. After 60°, the theoretical value of the time period showed great difference when compared to the measured value of the time period. It can be seen that the measured value of the time period at 80° is 3.0773s whereas the theoretical value of the time period at 80° is 2.7668s. The difference in the values are due to the uncertainty.When the pendulum swings, there is one true value of the period. Again, the time for one complete swing remains the same even as the size of the swing changes. Any attempted measurement of the period is an approximation of the true value, no matter how precise the instrumentation, no matter the method of measurement will give values close to each other. Therefore, the above equation shows that the time period of the pendulum is dependent on the angle of the pendulum.
In this formula, L is the length of the string and g is the acceleration due to gravity (about 9.8 m/s^2) and x is the angle of the pendulum. From this equation, it can be seen that only factor that affect the period of a simple pendulum are its length, the acceleration due to gravity and the angle of the pendulum. The period is completely independent of other factors, such as mass.
It was seen in the experiment that the measured value of time period was almost similar to the theoretical value of the time period up to the 60° angle of the pendulum. After 60°, the theoretical value of the time period showed great difference when compared to the measured value of the time period. It can be seen that the measured value of the time period at 80° is 3.0773s whereas the theoretical value of the time period at 80° is 2.7668s. The difference in the values are due to the uncertainty.When the pendulum swings, there is one true value of the period. Again, the time for one complete swing remains the same even as the size of the swing changes. Any attempted measurement of the period is an approximation of the true value, no matter how precise the instrumentation, no matter the method of measurement will give values close to each other. Therefore, the above equation shows that the time period of the pendulum is dependent on the angle of the pendulum.
Sources Of Error
The possible significant experimental sources of error are the two 75 g masses not placed at the end of the rod. and oscillating the pendulum at different heights after each angle.
The possible significant experimental sources of error are the two 75 g masses not placed at the end of the rod. and oscillating the pendulum at different heights after each angle.
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Pendulum Excel Regression | |
File Size: | 11 kb |
File Type: | xlsx |
Extension questions
Q1) Make a plot of vs and use the slope to extract the value of g. Compare this to the accepted value.
The value of g found from the slope of this graph is different than the actual value which is 9.8m/s^2. The value of slope found through this graph is 1.6m/s^2. The slope of the line is equal to 4π^2/g (THE PENDULUM, n.d.) g is found to be 11.9 m/s^2. Perhaps the value of g is different because the value of g changes slightly at different places on earth.
Q2) What would the period be if the pendulum had been inclined to 90 degrees? What value of g does this correspond to?
If the pendulum was inclined to 90 degrees incline there would be no motion in the oscillation of pendulum. The period of the pendulum be 0. Since the only force affecting the motion of pendulum is mg cos θ. When the angle becomes 0, cos θ also becomes 0 thus resulting in no gravitational force in the mg cos θ.
Q2) What would the period be if the pendulum had been inclined to 90 degrees? What value of g does this correspond to?
If the pendulum was inclined to 90 degrees incline there would be no motion in the oscillation of pendulum. The period of the pendulum be 0. Since the only force affecting the motion of pendulum is mg cos θ. When the angle becomes 0, cos θ also becomes 0 thus resulting in no gravitational force in the mg cos θ.
reference list
THE PENDULUM. (n.d.). Retrieved November 26, 2014, from http://www.haverford.edu/educ/knight-booklet/pendulum.html