IN AN ELASTIC COLLISION 11/17/95
GOAL: To test whether the laws of conservation of linear momentum and
conservation of kinetic energy hold during a collision of two magnetic pucks on the air table.
READING: Giancoli chapters 6-7
PROCEDURE: We will analyze only the elastic collision of the two magnetic pucks of non-equal mass (collision A from lab A11).
Some general guidelines:
1) Measure everything as carefully as possible; otherwise, you will be disappointed in your final results.
2) Three significant figures ought to be possible for many measurements; perhaps only two in other cases. Use your judgment.
3) Consider the spark rate of 20 Hz to really mean 20.0 Hz.
4) Use the following units: kilograms for mass; cm/sec for speed.
5) Use the mnemonic subscripts H and L for heavy and light puck; i and f for initial and final quantities.
A) Determination of the initial and final speeds of the heavy and light
pucks and the CM.
Each of the two puck tracks should begin and end with a straight-line portion of at least six equally-spaced sparks, indicative of constant initial and final puck velocities. You should also be able to determine the initial and final speed of the CM from these SAME sets of sparks. On the actual air-table paper, neatly and clearly show the calculation of each of these 6 speeds; do the calculation near the appropriate set of sparks. In your journal, create and fill in a table like the one below with your results.
initial final
light vLi = vLf =
heavy vHi = vHf =
CM vCMi = vCMf =
B)
Determination of x- and y-components of velocity for each puck and the CM.
1) First, choose an x-axis direction. A convenient one would be along the direction of initial velocity of one of the pucks. In this case, this particular velocity vector would have no y-component.
See sample data sheet!
2) Clearly label the x-axis that you choose on your spark paper, and be sure to define and label the positive x direction.
3) The y-axis must be chosen so that it is EXACTLY perpendicular to the x-axis. Label the positive y-direction clearly on your spark paper.
4) CAREFULLY measure the angle of each of the four puck velocity vectors with respect to either the x- or y-axis. Clearly label the angles on the spark paper, and then use these angles and the speeds from the previous table to find the x- and y-components of each of these four puck velocities. Be sure to include negative signs where appropriate on the velocity components; your calculator will not give you the correct signs!
Again, see sample data sheet.
5) As in 4 above, use (and label) the appropriate angles and the corresponding speeds to find the velocity components for the CM.
6) In your journal, record your results in tables like the ones below (YOU add the units!).
INITIAL FINAL
vi [[the vxi vyi vf [[the vxf vyf
ta]]i ta]]f
light light
heavy heavy
CM CM
C) TESTING FOR CONSERVATION OF X- AND Y-MOMENTA
Each partner must perform the following calculations independently. Partners should compare answers only after independent calculations. This procedure will help prevent calculation blunders. Values should be recorded in tables like those below, except you need to add units.
1) Using the data from part B, calculate the initial and final x-momentum and the initial and final y-momentum of each puck. Use these values to determine a total value of initial and final px and py
2) Use the center of mass initial and final x- and y-velocity components found in B to calculate the initial and final x- and y-momenta of the CM.
initial final
mass vx px vx px
light
heavy
total XXXX XXX XXX
CM
initial final
mass vy py vy py
light
heavy
total XXXX XXX XXX
CM
3) How close are the total initial and final x-momenta (% difference)?
4) How close are the total initial and final y-momenta?
5) How closely does the x-momentum of the CM match the x-momentum determined by summing the x-momenta of the two masses? Should these values match? why? (and same questions for the y-momentum)
6) List all the external forces that operated on the masses during this
experiment. Which forces could not have changed the system's momentum? Why?
Which forces could have changed the system's momentum? Why?
7) If you were to examine collision B from lab A11, should you find that x- and y-momentum was conserved? Why or why not?
D) TESTING FOR CONSERVATION OF KINETIC ENERGY
1) Use the known initial and final speeds of the two masses to determine the initial and final kinetic energies of each puck. Record your results in a table like the one below. Determine the initial and final kinetic energies of the two-puck system. As before, each partner should work independently; the results should then be compared.
initial final
mass v KE v KE
light
heavy
total XXXX XXX XXX
2) Why didn't we worry about x- and y-component speeds in this part as we
did with momentum in the previous parts?
3) To what extent (i.e., percent difference) was kinetic energy conserved? Should kinetic energy actually have been conserved in this collision? Why or why not? If you were to examine collision B from lab A11, should you find that kinetic energy was conserved? Why or why not?