VALIDITY OF THE LAWS OF MECHANICS
IN DIFFERENT INERTIAL REFERENCE FRAMES
1. Ideal two-dimensional motion:
Download the computer program Billiard to disc. Save the Borland Graphical Interface unit on the same disc.
Billiard simulates a two-dimensional collision as viewed in different reference frames. For some choice of initial speed and impact parameter, record the initial and final components of velocity, momentum, and kinetic energy. Find the velocity components in the center-of-mass frame (calculate them yourself) and verify that momentum and kinetic energy are conserved in that frame as well. Do the total momentum and total kinetic energy have the same value in both frames? Compare your calculations to the computer's.
2. Actual two-dimensional motion: You will be colliding two pucks on an air table and quantifying their motion before and after their collision. First verify that the air table is nearly level. If not, adjust it with the three leveling knobs. Take a strobe photo of two colliding pucks of different sizes. Measure their masses.
3. Digitizing two-dimensional data: Convert your picture into data: use a scanner to create a graphics file, then use Microsoft Paint or another graphics program to locate the pixel coordinates of the center of each image of both pucks.
4. Analyzing two-dimensional data: Calculate four velocities -- the 'before' and 'after' velocities of both pucks. Since the velocity in a plane is a two-dimensional quantity, this makes for eight quantities you need to measure -- v1x, v1y, v2x, v2y, v'1x, v'1y, v'2x, and v'2y. Make a table with three rows -- Puck 1, Puck 2, and TOTAL -- and five columns -- vx, vy, px, py, and KE -- for the initial values of these quantities. To the right of this table, make an identical table for the same quantities after the collision. Calculate all these quantities, looking to see if total momentum and total kinetic energy are conserved.
5. Transforming to another frame: You are now ready to transfer your data into a different reference frame. Make another set of tables, like the ones above, in your notes. Find the center-of-mass velocity from
vcmx= (m1v1x + m2v2x) / (m1 + m2)
vcmy= (m1v1y + m2v2y) / (m1 + m2)
Next, subtract off the center-of-mass velocity components from the velocity components you measured before. Now see whether total momentum and total kinetic energy are conserved.
For next time: In preparation for the next experiment, do your library work: Go to the library and find at least one reference to the Michelson-Morley experiment. Take notes. You will want to understand what is going on, to know any useful formulae associated with the experiment, and understand the point of the experiment. Once you have done this, come back to the lab and show your instructor the reference from which you got this stuff.