This report will investigate the theoretical
velocity of a ball bearing gun. The

methods and techniques used to derive the
results will be shown along with the

possible systematic and random errors
caused by experimental limitations.

Discussion: · Since the track is
virtually frictionless and air resistance is

neglected, the system is
isolated; the net resultant force of the external

forces equals zero. · The
total linear momentum of the system before the

collision is equal to the
total momentum after the collision. Therefore, the

total change in momentum
of this two-particle system is zero. · Equation that

represents the
conservation of momentum: · The total linear momentum of an

isolated system
is constant. · All significant experimental errors have been

incorporated
into the final velocity result. Aim: To investigate and determine

the muzzle
velocity of a ball bearing gun by utilizing the law of conservation

of
momentum. Determine out the theoretical velocity using various
mathematical

methods and techniques. Hypothesis: This two-particle system is
virtually

isolated, thus the total change in momentum is zero. Therefore when
the two

bodies collide, they will exert forces on each other, equal in
magnitude but

opposite in direction. Resulting in one combined body that is
equal to the sum

of the momentum of the two particles before the collision.
Materials: · One (1)

Ball bearing. (Weight - 65.9g 0.1, Approx Size - 2cm
in diameter) This will be

the projectile that is fired from the missile
launcher. · One (1) Cart. (Weight

- 678.3g 0.1) This will be the object on
which the projectile is fired onto. ·

One (1) standard Stopwatch. (Can
measure up to 100th of a second) Used to time

the journey of Cart + ball
bearing. · One (1) Track. (Measuring device length -

0.50m 0.05) Used to
guide cart and measure displacement. Method/Procedure: 1.

Prepare track
by aligning it and the cart to a perfect 180 degrees to the

launcher. ·
Distance used was 0.50m 0.05. 2. Fire the ball bearing into the

cart and time
the journey. · The ball bearing used in this experiment, took an

average of
1.14 0.1 seconds to complete 0.50 meters. 3. Work out the
theoretical

velocity of the ball bearing in the barrel of the launcher. ·
Equations used to

determine theoretical final velocity: - - NOTE: During
entire experiment, safety

glasses are to be worn. Any spectator that is not
wearing safety glasses should

watch from a safe distance. Results: Errors
accounted for: · Parallax Error:

0.05m · Stopwatch/Timing Error: 0.1s ·
Mass measurement error: 0.1g Recorded

measurements (NOT including
uncertainty): Times for overall journey: 1.13s,

1.13s, and 1.16s
Distance: 0.50m Mass of Ball Bearing: 65.9g Mass of Cart:

678.3g To
determine average time (NOT including uncertainty): To determine mass

of
combined body after collision: To determine velocity of combined body
after

collision: s = 0.50m 0.05 t = 1.14s 0.1 s = 0.50m 10% t = 1.14 8.7% To
determine

velocity of ball bearing in barrel of missile launcher: The muzzle
velocity of

this ball bearing gun is: . Errors not incorporated into method:
· The ball

beating itself has a small drag coefficient, although the cart,
which the ball

bearing is fired into, may experience air friction. · All
air

friction/resistance was neglected. Conclusion: This experiment proved
my

hypothesis correct. Throughout the entire experiment the overall change
in

momentum equaled zero. When the two particles collided there momentum
was

conserved resulting in one body that was the combined mass and momentum
of the

previous bodies. The result was obtained by recognizing that the
initial

velocity/momentum of the ball bearing could be determined by
utilizing the

conservation of momentum law; that as long as the net resultant
external forces

equal zero, the momentum will be constant. From this exercise
I learnt new

method and techniques used in calculating errors and
uncertainty.