6/3 Physical Pendulum

Purpose: The purpose of the lab was to derive expressions for the period of various physical pendulums and to verify predicted periods by experiment. 

Procedure:

The first part of this experiment was to derive an expression for the period of the physical pendulums of an isosceles triangle oscillating about (a) its apex and (b) the midpoint of its base. We knew that we would need the center of mass of the triangle and the inertia of each position, so we started by finding these (FIGURE (1),(2),&(3)).

FIGURE (1)

FIGURE (2)

FIGURE (3)

Then we set up the equation for torque (I · α; where I = inertia and α= angular acceleration). Once we solved for α, we were able to calculate ω and determine the period of oscillation. (FIGURE (4)).

FIGURE (4)

After we found our theoretical values we were ready to find the experimental values. We set up the pendulums as shown in FIGURE (5).

FIGURE (5)

 We used a photogate to capture the period of the pendulum. When we did that we came up with the periods in FIGURE (6) and FIGURE (7).

FIGURE (6)

FIGURE (7)

The period in case (a) was 0.783 and the period in case (b) was .658.

Conclusion:
Our theoretical value for case a was very close to our experimental value; it was approximately 0.1% different than the theoretical value. For case b, the experimental value was farther off; it was around 1% different than the theoretical value.

Since the experimental values are in close agreement with the theoretical values, we can conclude that theory provides a good description of the physical behavior of a pendulum.

Sources of error in this lab could come from making theta larger than it needed to be, because the period we calculated was for a very small theta. Of course, there are always random errors that are difficult to explain but in this experiment were small. 

5/20 Conservation of Energy/ Conservation of Angular Momentum

Purpose: To prove conservation of energy and angular momentum using a collision with a meter stick and clay.

Procedure:
To prove conservation of momentum we needed to demonstrate a rotational collision. To do this, we set up a meterstick, pivoted at 1.3 cm, to collide with clay where the clay sticks to the meter stick stick after. We then set up a camera to capture the collision. Once we had the meterstick-clay system setup, we raised the meter stick to the horizontal position and let it fall straight down (FIGURE (1)).

FIGURE (1)

We recorded the collision (video to right) and analyzed it in LoggerPro (FIGURE (3)). Our analysis concluded that the meter stick-clay system pivoted to a height of 27.79 cm above its original position. 

FIGURE (3)

We then calculated the height with energy and momentum (FIGURE (4)). We first had to calculate the initial angular velocity of the meter stick using conservation of energy. Once we had the initial angular velocity of the stick we used angular momentum to calculate omega right after the meter stick hit the clay. We then used energy again to solve for the final height it would reach. We came up with a value of 0.286 m.

FIGURE (4)

Conclusion:
Overall, the experiment seemed to prove the theory we had correct. Out calculated value was about 2% off from out experimental value, which is good since there could have been a few sources of error. One source of error could be from the camera. The camera is not very high quality and had a slight fish-eye so the image is slightly distorted. The image is also not very focused so it is difficult to pin-point the exact origin and the final position. There also might have been some friction in the system.