What factors affect the period of a pendulum\
how to calculate the acceleration g using a pendulum
When Galileo was only 17 years old, he used his pulse to find the period of a
swinging lamp in the Cathedral of Pisa and discovered the law upon which pendulum are built.
THis illustrates the power of a lab. Physics is not just pugging numbers into equations !
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Let's suppose the angle is small. The bob swings back and forth and there is no air resistance.
1) label the vectors. Use: W the weight, Wx (x-component of the weight), Wy (y-component of the weight) and N the normal.
2) Along the y-axis, there is no acceleration so ______________________ is balancing the ______________.
3) Along the x-axis there is an acceleration. The bob speeds up as it falls (from far right to equilibrium position), slows down as it rises again (to far left), come to a rest (far left) , then speeds up again going down. Along the X-axis Fnet = _____________. (use m,g and a trig function with θ inside).
So the force acting on the bob to bring him back to θ =0 is just : Wx ? Wy ? N ? . This is the restoring force for a pendulum.
4) Mathematically you can show that if an angle is small then: sin (θ ) =θ. In that case. Fnet = Fx = _________.
You just have shown that the restoring force Fnet is proportional to _________________. Therefore, a pendulum undergoes simple harmonic motion.
5)A complete vibration (any back-and-forth motion ) is called a cycle. A cycle is the movement from some point (say the far right), to a maximum displacement in the other direction (say the far left) then back to the same point again (far right). The period (T) is the time to complete one cycle. For example, suppose 3s is required for a bob to swing back and forth, then the period of this vibration is T = ____________.
6) The number of cycles per second is called the frequency (f) . frequency = 1/ period. The unit is hertz. So if T= 3s, then the frequency = ___________.
7) The length (L) of the pendulum is measured from the point of suspension to the center of the bob. Since the bob has a radius,
L = length of the string + radius of the bob. Using a caliper measure the diameter then the radius of the bob: R = ___________________.
PURPOSE
The purpose of this lab is to investigate what factors influence the period of a pendulum. Take some guesses:
8) Do you think the mass will affect the period T? ____________ why ? ___________________________________________________________
Do you think the length of the pendulum will affect the period ? ________________________________________________________
Do you think the amplitude (the angle θ) will affect the period ? ______________________________________
Do you think a pendulum can help you to take decision?__________ finding water ? __________ find out your final grade in Physics ? __________
We will also investigate ways to estimate the acceleration due to gravity g = 9.8m/s/s using a pendulum.
PROCEDURE
step 1: Let's investigate if weight influences the period of a pendulum. Use different masses (we have only 2 here) for bobs and adjust each so the string is 100cm from the pivot point to the center of gravity of the bob. Pull the bob back to make an arc of about 15 degrees. (use a protractor). RElease and count the number of vibrations (one vibration is one complete back-and-forth movement) for exactly 1 minute. The arc, length of pendulum, and all other variables must be the same. THe only difference should be the mass of the bob. Take three trials for each mass and average the findings. Record all data in table 1. Also record the mass of each bob (a metal one and wooden one)
TABLE 1
A simple pendulum consists of a mass, called a bob, connected to the end of a suspended string. When the bob is
pulled to one side of its position of rest and then released, it begins
to vibrate in a simple harmonic motion. We suppose the angle to be
small. Each time we have a simple harmonic motion the displacement (here the displacement is angular = θ)
Let's suppose the angle is small. The bob swings back and forth and there is no air resistance.
1) label the vectors. Use: W the weight, Wx (x-component of the weight), Wy (y-component of the weight) and N the normal.
2) Along the y-axis, there is no acceleration so ______________________ is balancing the ______________.
3) Along the x-axis there is an acceleration. The bob speeds up as it falls (from far right to equilibrium position), slows down as it rises again (to far left), come to a rest (far left) , then speeds up again going down. Along the X-axis Fnet = _____________. (use m,g and a trig function with θ inside).
So the force acting on the bob to bring him back to θ =0 is just : Wx ? Wy ? N ? . This is the restoring force for a pendulum.
4) Mathematically you can show that if an angle is small then: sin (θ ) =θ. In that case. Fnet = Fx = _________.
You just have shown that the restoring force Fnet is proportional to _________________. Therefore, a pendulum undergoes simple harmonic motion.
5)A complete vibration (any back-and-forth motion ) is called a cycle. A cycle is the movement from some point (say the far right), to a maximum displacement in the other direction (say the far left) then back to the same point again (far right). The period (T) is the time to complete one cycle. For example, suppose 3s is required for a bob to swing back and forth, then the period of this vibration is T = ____________.
6) The number of cycles per second is called the frequency (f) . frequency = 1/ period. The unit is hertz. So if T= 3s, then the frequency = ___________.
7) The length (L) of the pendulum is measured from the point of suspension to the center of the bob. Since the bob has a radius,
L = length of the string + radius of the bob. Using a caliper measure the diameter then the radius of the bob: R = ___________________.
PURPOSE
The purpose of this lab is to investigate what factors influence the period of a pendulum. Take some guesses:
8) Do you think the mass will affect the period T? ____________ why ? ___________________________________________________________
Do you think the length of the pendulum will affect the period ? ________________________________________________________
Do you think the amplitude (the angle θ) will affect the period ? ______________________________________
Do you think a pendulum can help you to take decision?__________ finding water ? __________ find out your final grade in Physics ? __________
We will also investigate ways to estimate the acceleration due to gravity g = 9.8m/s/s using a pendulum.
PROCEDURE
step 1: Let's investigate if weight influences the period of a pendulum. Use different masses (we have only 2 here) for bobs and adjust each so the string is 100cm from the pivot point to the center of gravity of the bob. Pull the bob back to make an arc of about 15 degrees. (use a protractor). RElease and count the number of vibrations (one vibration is one complete back-and-forth movement) for exactly 1 minute. The arc, length of pendulum, and all other variables must be the same. THe only difference should be the mass of the bob. Take three trials for each mass and average the findings. Record all data in table 1. Also record the mass of each bob (a metal one and wooden one)
TABLE 1
| bob description (find |