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.