2015年6月4日星期四

June-3-2015 Lab 20: Physics Pendulum

Lab 20

Purpose:Derive expressions for the period of various physical verify your prediction periods by experiment.


Apparatus:

1)A photo gate determine the period of the oscillation.

2)A laptop with logger pro

3)Holder that can fix the object do the pendulum.

4)This set up can find the period of each object oscillating. 





Steps:


1. Find isosceles triangle, a semicircular plate, and a ring, then do five different experiments. At each experiment, set top and bottom as pivot on triangle and semicircular plate, and ring.




























2.Experiments

  Do five each experiments with triangle, ring, and circular.
  Fix the triangle, ring or circular at the pivot point then release it at some very small angle and let it go and using the laptop to collect their period.






  This is how it will looks like when doing a experiment. 
  Record the period of each experiment and mark it for confusing.

3. Prediction

  To predict the period of them, Finding the moment of inertia and set up the equation of oscillation then get the angular velocity, and that's how to find out the period.

  1)For each with different pivot, they have different moment of inertia. Using the parallel axis theorem to find I.
   First of all, find the center of mass and calculate the moment of inertia of center of mass as pivot.Then, using the parallel axis theorem to find the moment of inertia of them.
  2)After knowing the moment of inertia, it's very easy to set up the oscillation equation. 
  (Note:For the oscillation equation, we need to find out the a smililar equation such like a = -kx)
   Knowing that Torque = (moment of inertia)* (angular acceleration)
   The torque is obvious with only gravity, and the angular acceleration can be represent with some angle.
   Also, the angular velocity w^2 = k, and period T = 2*pi/w
   And this how to find period.


Example:

  Here is some example of this lab.


1.Experiment results
  Those are the period of each experiment.

  1)First one is the triangle with bottom as pivot, and it gives period T=0.604s.




 2)Second one is the triangle as top with pivot.
  Period T = 0.6996s 








  3) This is the circle, and the pivot is top. Period T = 0.3740s





  4) This is the circle, and the pivot is bottom. Period T = 0.7432s


  5) This is the ring. Period T = 0.7218s

2. Prediction
  In order to find the moment of inertia, it's necessary to find the moment of inertia of center of mass.

 1) Triangle

  •   This is how to find the center of mass of iso triangle

  •   This is how to find the moment of inertia of center of mass


  •   Using parallel-axis theorem to find the moment of inertia of different pivot.


  •   Then using all the results to find the period. 

Uncertainty of the period is less than 1 percent.

  2) Semicircular plate:

  •   This is how to find the center of mass of Semicircular plate


  •   This is how to find the moment of inertia of center of mass


  •   Using parallel-axis theorem to find the moment of inertia of different pivot.
  •  Then using all the results to find the period.


Uncertainty of the period is less than 1 percent.

  3) Ring:

 This is how to find the moment of inertia of total
 Then using all the results to find the period


After comparing the experiments results and prediction results.
Uncertainty of them are less 1 percent off.


Conclusion:

This lab is about physics pendulum which gives period in experiment and in prediction. To finish this experiments we set up the equipment and find the period in experiment and compare it with the result we got in prediction. 
Given the uncertainty is very small, and results are good.

June-1-2015 Lab19: Conservation of Energy/Conservation of angular Momentum

Lab 19

Purpose: By using conservation of Energy and conservation of angular momentum to test how high a meter stick and clay will go after they stick together.

Apparatus:

1. One meter stick and sticky clay with some mass.
2. Laptop with video capture option.
3. A Holder can fix the meter stick.
4. Fix the top as pivot.



Steps:

1.Measure the mass of meter stick, and clay mass.

2.Set up the equipment, and start to capture the process.

  1).Set the meter stick to horizontal position and let it go.
  2).Meter stick and clay stick together when it reach the bottom of swing and collides in elastically.
  3).Reach and rotate together at some height.
  4).Find the height by using laptop and video capture.

Prediction:

 To compare our results accuracy, it can be shown by assuming energy and angular momentum are conserved during the whole process.

  First scene: meter stick with gravitational energy exchange to angular velocity at bottom of swing and hit the clay with inelastic collision. 
  Because the meter stick is swing and rotating, so we have to find out the momentum of inertia of the meter stick as pivot at top
  
  By knowing how height the meter stick is and mass of them, using conversation of energy to find the angular velocity of meter stick at bottom.
(Note: Meter stick is not one small ball, so center mass of meter stick should at middle. To find the velocity should be 2mg/h = 1/2*Iw^2

  Then using conversation of angular momentum find out the velocity after collision which by the way is IstickW = Itotal*Wf

 Second scene: Meter stick and clay stick together and go some height and stop.
  After collision, using conversation of energy again. Angular velocity of the meter stick and clay exchange to the gravitational energy.
  (Note: the moment of inertia is not the one before, it's a new because this time it has clay on it.)
  And find the how height they went together.

  Comparing the two results.

Example:

  1)The mass of meter stick and clay, and length of meter stick.
  2)video capture and result of height at laptop.
Which gives H = 0.279m
(Note: the length of stick is not 1 meter because the hole at the top is not exact. so may set the meter lenght to 0.98 m)
  3)Prediction
  •   moment of inertia of stick
  • gravitational energy exchange to angular velocity
It gives angular velocity of stick at bottom is 5.81 rad/s
  • After collision
It gives angular velocity of stick and clay at bottom is 2.6499 rad/s

  • How height it went by predict.

It gives h = 0.28024 m

  • Uncertainty.

Conclusion:
 This lab is to use the energy and angular momentum conserved to find out the height of meter stick and clay go up. To check out prediction result, we set up a experiment and find the height in experiment, then compare those two results gives uncertainty is 0.44 % off. 

Source of uncertainty:

  •   in the experiment, when the meter stick and clay stick together may lose energy.
  • Air resistance will cause some energy lose.
  • The original position when release the meter stick may not accurate.

2015年5月14日星期四

May - 13 - 2015 Lab18 : Finding the Moment of Inertia of a Uniform Triangle Rotating about it's Center of Mass

Lab 18

Purpose: To determine the moment of inertia of a right triangular thin plate around it's center of mass, for two perpendicular orientations of the triangle.

How to find out moment of inertia of right triangular is what about of this lab. I am going to use one specify equipment to do it today.
Why we chose this equipment because it can give the angular acceleration of the disk. By knowing the angular acceleration , we can use the formula I = a * r calculate the moment of inertia. Thus, The moment of inertia of triangular is the moment of inertia of disk with triangular minus the moment of inertia of disk without the triangular.

Apparatus: 

Connecting the top disk to computer only and set the disk will spin independently and bottom one stops. 

Change the disk to 200 counts per rotating.  

weight of disk is 1.36 kg
radius of disk is 0.0625 m
hanging mass is 0.025 kg
Large pulley radius is 0.0495 m.
Triangular long side b = 0.1485 m
Triangular short side a = 0.098 m
weight of triangular 0.455 kg
Those data will be used on next steps.

turn on the air so the top disk can rotate, then Start collect on the computer and record the radius and distance on computer.

Those are two experiment should be down, one triangular is at right, one is at bottom. 




Part 1

Part 1 is to find out the moment of inertia with those two pose around it's center of mass.

To find out the moment of inertia.

do three experiment, one is without triangular, one is with triangular, and another one is with triangular with different face. 
Record the up and down angular acceleration. 
Because disk have friction, so up and down accelerations will be different.



By using this equipment, we can find the Angular acceleration up and down with three different condition. 
And then use them to find the moment of inertia of disk with those different conditions.





















That's equation we use to find out the moment of inertia.
Why we need to find out the moment of inertia is that The moment of inertia of triangular is the moment of inertia of disk with triangular minus the moment of inertia of disk without the triangular.
so we can find the uniform triangular by using this method.

Then collect the data.
Those graphs are the one without triangular and one with triangle with long side pointing up.

They are angular velocity vs time graph. So the slope of the line are angular acceleration.















Plug the data into the function which can find the moment of inertia

After calculate, moment of inertia of disk with triangular is 0.0028551 kg*m^2

the moment of inertia of disk without the triangular is 0.0026006

Therefore, moment of inertia of triangular rotating aroung the center of mass is 0.0002545 kg * M ^2







Using the same method, find out the another condition's moment of inertia of triangular. 








So the moment of inertia of triangular in this pose is 0.0054888 kg* m^2.

In part 1, I obtain the two different moment of inertia around it's center of mass which are 0.0054888 kg* m^2 and 0.0002545 kg * M ^2.


Part 2

Part two is to test our results.

If without the experiment, it's very difficult to find out the moment of inertia around it's center of mass, so need to change the way to calculate them.

If not around the center of mass but around one side.



By around the one edge of the triangular.







it's easy to find I paralle axis and M(d).; thus, the moment of inertia around it's center of mass is just I paralle axis - M(d)






To find I paralle axis and M(d). 
After calculation
Moment of inertia around center of mass is just the (1/18) *M* a^2 for this

another will be (1/18) *M* b^2

So for the first one
















Moment of inertia around center of mass is 0.000242768 kg* m^2 
Uncertainty compare to the value got on the experiment is 4.8 % off.


Another one:




Moment of inertia around center of mass is 0.000557432 kg* m^2 
Uncertainty compare to the value got on the experiment is 1.53 % off.

Conclusion:

This is the lab about how to find out the moment of inertia of a uniform triangular rotating about it's center of mass. By using formula and measurement, we find the experiment value and compare with the prediction value to see how well the results are. With friction, mistakes, and not advanced equipment our results are off by 1.53% and 4.8% are good results.