# WORD ```Lab 4: Conservation of Linear Momentum in Collisions
Objective
Determine whether linear momentum is conserved for a particular
experimental system within the uncertainties of the measurements.
Pre-lab
None
Lab Style
Cookbook
Experimental System
A ball rolls down a curved ramp until it reaches a plateau. The ball
continues rolling until it strikes a stationary ball at the very end of the ramp. The
stationary ball is well aligned with the incoming ball as far as height is concerned
(we will call this the z axis), but it may be off-center in the x-y plane.
Immediately after the collision, both balls fly off in the x-y plane. We will find if
the total linear momentum immediately before the collision was the same as the
total linear momentum immediately after the collision.
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1 aluminum ramp
1 test tube holder
1 wooden placement block
1 screw
2 steel balls
1 plastic ball
One wooden block
1 sheet of carbon paper
Tape
1 meter stick
1 plastic ruler
C clamps
Experimental Technique
Last week we rolled a ball down a curved ramp and studied whether the
kinetic energy of the ball as it left the ramp was the same as the initial potential
energy of our system. This week we will use a similar set up to determine whether
linear momentum is conserved in collisions as the balls leave the ramp.
Remember that momentum is a vector quantity, so magnitude and direction are
both important!
Part 1: Axes and Initial momentum
To set up your axes, place a piece of grid paper on the floor and drop a
plum-bob through the small hole in the base of the ramp as you did last week to
mark the origin. You may want to align the origin with one of the grid point.
Draw two mutually perpendicular lines and label one of them the x-axis and the
other the y-axis. The orientations of the axes are not important (any set of
coordinate axes is equally valid).
Measure the mass of one steel ball. Release the ball from the highest
position and record where it lands. Take several trials; at least 5, no more than
10. Use the measured x and y positions and the height of free fall to determine
the velocity vector (x and y components) of the ball (similar to last week). In
your data analysis, you willl calculate the average initial momentum and the
standard deviation from your measurements; do forget to propagate errors.
Part 2: Final Momentum
Weigh the target ball and then place it at the end of the ramp. Release the
steel ball ( m1) from the same position as in part one. The target ball ( m2 ) will
have several different configurations:
1) A steel ball, placed on a dimpled wooden block at the very end of the
ramp and slightly off-center. Be sure to raise the wooden block to a
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height such that the incoming ball and the stationary
2) A plastic ball, placed on a dimpled wooden block at the very end of
the ramp and slightly off-center
In each of these cases you should record the final x and y displacements of
BOTH balls. You should also label the dots after each trial so that you can tell
which dots belong to which collision. Use kinematic equations to relate the final
displacements of each ball to its velocity right after the collision and then use that
information to see if linear momentum was conserved. Do at least five trials for
each configuration.
Data analysis and writeup
Analyze your data (being sure to propagate uncertainty) and then compare
your initial and final momentua (in both x and y directions) and see if linear
momentum conserved. Also check if kinetic energy is conserved. Measure the
angle between the final velocity vectors of m1 and m2 for the first case ( m1  m2),
is this angle near 90o (90o is the theoretical result for elastic collision of m1  m2
and m2 initially at rest.)
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