17-Nov-2014: Angular Momentum with Collision

Purpose:
Find the relationship between angular moment and height in an inelastic collision.

Apparatus:
The system that the experiment was conducted on consisted of a meter stick with a hole drilled on one of its far ends. The meter stick was then suspended by its hole allowing it to oscillate.

At the meter stick's lowest point was located a small piece of clay. When the meter stick where lift at any angle it would collide with the clay in an inelastic collision.

 A camera was set in a position to record the movement of the meter stick before and after the collision.

Experiment:
To begin the experiment, we needed to make a prediction for the max height of the clay after it collided with the bar, releasing it 90 degrees from the clay's position. In order to do this we need to derive an expression for the height of clay at each time interval and measure the mass of the clay and meter stick. This is done using the equation conservation of angular momentum:

Inertiabefore * angular velocitybefore = Inertiaafter * angular velocityafter

Moment of Inertia of bar on its end = (1/3) MR^2

Moment of Inertia of a particle = MR^2

The conservation of angular momentum gives us a value for the angular velocity when the meter stick collides with the clay. This value can be used in the conservation of energy where we would have rotational kinetic energy when the clay and meter stick collide and gravitation potential energy when the clay reaches its maximum height. The conservation of energy then gives us an angle value. With this angle, 59.56 degrees, we are able to find the max height of the clay. We can determine that the meter stick produces a right triangle when its not positioned at rest meaning that we can subtract the length of the meter stick to the side adjacent to the angle we predicted meaning:

Height = Length - Length * cos (angle)

Height = 1 - cos (59.56)

Height = 0.49 meters

Now that we have a theoretical value for the max height of the clay after it collides with the meter stick we can find the actual height.

By connecting our camera to a laptop and opening logger pro we are able to place points on the position of the meter stick as it collides with the clay and reaches its max height constructing these graphs:

Unfortunately this height is not correct since the clay is slightly elevated but it is quickly fixed by subtracting the elevation with the max height recorded by the camera, giving us the value:

Experimental Maximum Height = 0.284 meters

Conclusion:
Many questions came to mind on why the theoretical value and experimental value of the height were so different. We checked all of our values and made sure they were correct. Finally we came to the conclusion that the meter stick experienced friction on its pivot point as well as air resistance as it moved.