Lab 18: Conservation of Energy and Angular Momentum

Physics Lab #18 started on 5/20/15
Conservation of Energy and Angular Momentum
Annemarie Branks
Professor Wolf

Objective: In a rotational system that experiences an inelastic collision, determine the height at which the bottom of the system experiences for one complete swing. Predict what the height ought to be according to the Conservation of Energy and Conservation of Angular Momentum theorems. Confirm these principles by comparing the calculated final height to the actual final height.

Procedure:
     1.  Set up a rotating system like the one shown below. We used a meter stick of 147 grams pivoted at 10 cm from the top. A clay mass was placed on the ground in such a way that when the meter stick was let go from the horizontal position, the two would collide. To ensure an inelastic collision, we wrapped tape around the clay and one end of the meter stick with the sticky side of the tape exposed. 

     2.  We want to determine if the Conservation of Energy and Conservation of Angular Momentum theorems are good for calculating the final height. The first part of the system's swing is its gravitational potential energy. That gravitational potential energy will turn into Kinetic Energy just before the meter stick hits the clay. We want to use rotational kinetic energy  which is equal to 0.5*I*ω^2. So before we set up our energy problem, we want to determine the meter stick's moment of inertia. Use the Parallel Axis Theorem, which states that it is equal to the object's Inertia about its center of mass plus its mass times the distance it moved squared, or I = Icm +Md^2. The moment of inertia for a rod about its center of mass is 1/12*ML^2. The pivot moved 0.4 meters from the center so our new moment of inertia is 0.0358 kg*m^2. The calculations for that value are shown below.

     3.  Now that we have Inertia of the meter stick, we can do a Conservation of Energy problem to find the angular speed just before it hits the clay. If the origin is set at the very bottom part of the meter stick's swing, then in this case the height is 0.9 meters. This then converts into Kinetic Energy and Gravitational Potential Energy. The height for the GPE is the distance of the center of mass to the origin on the down swing, which in this case is 0.5 meters. Here are our calculations for finding ω which came out to 5.68 rad/s.

     4.  Using the initial ω in a Conservation of Angular Momentum problem, we can final final ω which comes from the meter stick colliding and sticking with the clay. Conservation of Angular Momentum tells us that Linitial = Lfinal which is the same as Iωinitial = Iωfinal. Below are the calculations for finding ωfinal which came out to be 3.47 rad/s.

     5.  The meter stick, along with the clay attached, will swing up to a certain height and to find that height we will need to use Conservation of Energy again. My lab partner and I had some difficulties with this part, but other people advised us that it would be easier to put zero GPE at the pivot. Below are the calculations to find h. 

     6.  So now that we have a calculated h of 0.384 meters, we can compare it to an actual value. With the system that has been set up, use a camera and video capture on LoggerPro. Start plotting data points from the frame where the meter sticks to the clay. Find the highest that the clay will reach when it momentarily has no kinetic energy.

The data set shows that the highest the clay at the end of the meter stick gets is 0.3651 meters. Our calculated height is larger than the actual height. The difference can be attributed to some sources of error and if we considered all these uncertainties, then we might be totally confident that the Conservation of Energy and Angular Momentum theorems work.

Sources of Error/Uncertainty:

• There was inaccuracy due to human error for plotting the data points using video capture.
• The camera had poor resolution and the swinging meter came out blurry making it difficult to the plot the points.
• We did no consider exactly where on the meter stick the clay was sticking to so its distance from the pivot may be inaccurate.
• The meter stick had a curve to it which affected the path of the moving meter stick. Depending on where it was curved in the stick this could have changed the actual center of mass for the meter stick thus changing its moment of Inertia.