Simple harmonic motion for a Physical Pendulum

Purpose: 
      Predict and verify the period of a solid ring and a semi-circle foam oscillating around a certain pivot.

Equipment:
      Photo-gate sensor and foam

Experiment:
    1. Set up the apparatus as the pictures show.
    2. Calculate the Inertia of the solid ring  around the pivot.
    3. Get the expression of angular acceleration and omega.
    4. Calculate the value of the period.
    5. Hanging the solid ring around the pivot, give a initial push so that the foam oscillate in a small angle. Record the period.
    6. Repeat the step with a different pivot and for the semi-circle foam.

Part A: a solid ring

Part B: a semi-circle foam

Conclusion:
     Theoretical Period of the solid ring: 0.72212 s

    Actual Period at the center of the circle:  0.721802 s

    Theoretical Period at the center of the semi-circle: 0.738501 s

    Actual Period at the center of the semi-circle:   0.739 s

    Theoretical Period :  0.741046 s

    Actual Period of the semi-circle at the top: 0.754 s

    We successfully predict and verify the period of a solid ring and a semi-circle foam  oscillating around a certain pivot.

Lab #19 Conservation of Energy/Conservation of Angular Momentum

Purpose:
      Calculate the height that the meter stick can reach after releasing from horizontal position and hitting the clay at the lowest point by applying the concept of conservation of angular momentum and energy.

Equipment:
      meter stick, clay, video capture

Experiment:
      1. Set up the apparatus as the pictures show.
      2. Calculate the theoretical value before doing the experiment.
      3. Put a clay at the lowest point of the meter stick's path.
      4. Release the meter stick from the horizontal position with the other end pinned.
      5. Record the motion and use LogPro to measure the highest point that the meter stick reaches.
      6. Compare the actual value to the theoretical value.

Conclusion:

      The angular momentum and energy is conserved.

Lab#18 Moment of Inertia and Frictional Torque

Purpose: 
      Calculate the moment of inertia and the frictional torque of a disk and apply the value to predict the motion of the system of the disk and the cart.

Equipment:
      A large metal disk, a video capture, a cart and a track.

Experiment:
      1. Set the video capture and the metal disk.
      2. Measure the radii of the small disks and the large disk, and read the mass of the disks.
      3. Calculate the mass of each disk by volume and calculate the moment of inertia by the equation I=1/2 m r^2.
      4. Spin the apparatus, use video capture to determine its angular acceleration as it slows down.
      5. Calculate the torque of friction by the equation of torque=inertia times angular acceleration.
      6. Calculate the acceleration of the system of the cart and the disk.
      7. Predict the time it needs to travel 1 meter.
      8. Do the experiment for three times and calculate the percent error.

Conclusion:

      Through our calculation, we get the theoretical time is 7.83 s.

Lab #17 Finding the moment of inertia of a uniform triangle

Finding the moment of inertia of uniform triangle
Xuhong Zhao
Partners' Name: Amber Li and Daniel Negrete
05/13/2015

Purpose:
      Determine the moment of inertia of a right triangle thin plate around its center of mass, for two perpendicular orientations of the triangle.

Equipment:
      Disk, holder, triangle, hanging mass, string, sensor.

Measurement of the dimension and mass:

• The mass of the steel disk is 1357 grams
• The mass of the triangular plate is 456 grams
• The mass of the hanging mass is 25 grams
• The mass of the holder is 25 grams 
• The mass of the pulley is 36 grams
• The radius of the rotating pulley is 2.5 cm
• The high of the triangular plate is 14.8 cm
• The width of the triangular plate is 9.85 cm

Experiment:
    1. Set up the apparatus as the pictures show. Mount the triangle on a holder and disk. The upper disk floats on a cushion of air. A string is wrapped around a pulley on top of and attached to the disk. A string is wrapped  around the pulley and goes over a freely- rotating pulley to a hanging mass. The tension in the string exerts a torque on the pulley- disk combination.
    2. Turn on the air track and let the hanging mass, tie the hanging mass with the disk without the triangle.
    3. Let go the hanging mass, take the average angular acceleration of descending and ascending.
    4. Put the triangle horizontally on the holder, and repeat step three.
    5. Put the triangle vertically on the holder, and repeat step three.
    6. Based on the hanging mass and the angular acceleration, calculate the moment of inertia of each situation, and use the inertia with triangle subtract the one without triangle to get the inertia of triangle alone.
      7. Compare the theoretical value to actual value.

Conclusion:

  In vertical position. we find the difference between the experimental moment of inertia and theoretical moment of inertia is 0.000246-0.000239=0.000007,  that is about 2.8% error.

    In Horizontal position, we find the difference between the experimental moment of inertia and theoretical moment of inertia is 0.000555-0.000557=-0.000002, that is about 0.36 % error.

    There are some error could effect our experience. First of all, measurement exist error. We ignored the friction. I believe that our % error being less than 3% is very reasonable.

Lab#16 Angular accleration

Purpose:

      Using different  mass of the top disk, different hanging mass and different torque pulley to see what factors affect the angular acceleration.


Apparatus:
      The diameter and mass of the top steel disk: 12.60 cm, 1356 g
      The diameter and mass of the bottom steel disk: 12.66 cm, 1348 g
      The diameter and mass of the top aluminum disk: 12.62 cm, 466 g
      The diameter and mass of the small torque pulley: 2.50 cm, 10.0 g
      The diameter and mass of the large torque pulley: 5.37 cm, 36.0 g
      The mass of the hanging mass supplied with apparatus:  26.0 g

Experiment:
      1. Set up the apparatus as the pictures show.

      2. Set up the Pasco rotational sensor and computer, set the equation on the sensor setting to 200 counts per rotation.
      3. Make sure the hose clamp on the bottom is open so that the bottom disk will rotate independently of the top disk when the drop pin is in place
      4. Turn on the compressed air so that the disks can rotate separately.
      5. Wrap the string around the torque pulley to the highest point, start measurements and release the mass.

     6. Use the graph of angular velocity vs. time to measure the angular acceleration of upward motion and downward motion.

    7. Follow the instruction and change the factors to get angular acceleration under each condition.

Result:

Conclusion:

      EXPTS  1,2, and 3: Effect of changing the hanging mass----the heavier the hanging mass, the larger the angular acceleration.     
      EXPTS 1 and 4: Effect of changing the radius and which the hanging mass exerts a torque----The larger the radius, the larger the angular acceleration.     
       EXPTS 4,5, and 6: Effect of changing the rotating mass----the lighter the rotating mass, the larger the angular acceleration.

Ballistic pendulum

Purpose:

    The purpose of this lab is to find the initial velocity of a projectile in a ballistic pendulum using the conservation of momentum and energy theorem.

Set  up:

Conclusion:

      The uncertainty in the initial velocity of the ball was very low (0.06%), proving that the experiment was successful and that the method used (conservation of energy and momentum) was an accurate method. The initial velocity of the block was 6.03 +/- 0.0358 m/s. 

Lab #15 Collisions in two dimensions

Purpose: Look at a two-dimensional collision and determine if momentum and energy are conserved.

• Steel ball with steel ball
• Steel ball with aluminum ball

Setup for the camera:

    Click on "Camera Settings", then "Adjustments"

    Click on "Image". Set Shutter to zero, set Exposure to Manual and reduce it, increase Gain so that we get a reasonable (albeit grainy) image from the camera.

Gently set the stationary ball on the leveled glass table. (We need to level the table first.) Aim th rolling ball so that it hits the side of the stationary ball. The balls should ideally roll off at some decent angle from one another.

• Grab the point to rotate the axes
• set Origin
• Add point series

Part 1: Two steel ball elastic collision

Part 2: one steel ball and one aluminium ball collision