Momentum And Collisions

     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.