# This determine the muzzle velocity of a ball

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.

Physics