This report will investigate the theoretical velocity of a ball bearing gun. Themethods and techniques used to derive the results will be shown along with thepossible systematic and random errors caused by experimental limitations.Discussion: Since the track is virtually frictionless and air resistance isneglected, the system is isolated; the net resultant force of the externalforces equals zero.
The total linear momentum of the system before thecollision is equal to the total momentum after the collision. Therefore, thetotal change in momentum of this two-particle system is zero. Equation thatrepresents the conservation of momentum: The total linear momentum of anisolated system is constant. All significant experimental errors have beenincorporated into the final velocity result. Aim: To investigate and determinethe muzzle velocity of a ball bearing gun by utilizing the law of conservationof momentum. Determine out the theoretical velocity using various mathematicalmethods and techniques. Hypothesis: This two-particle system is virtuallyisolated, thus the total change in momentum is zero.
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Therefore when the twobodies collide, they will exert forces on each other, equal in magnitude butopposite in direction. Resulting in one combined body that is equal to the sumof 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 bethe 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 timethe 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 thelauncher. Distance used was 0.50m 0.05.
2. Fire the ball bearing into thecart and time the journey. The ball bearing used in this experiment, took anaverage of 1.
14 0.1 seconds to complete 0.50 meters. 3. Work out the theoreticalvelocity of the ball bearing in the barrel of the launcher. Equations used todetermine theoretical final velocity: – – NOTE: During entire experiment, safetyglasses are to be worn. Any spectator that is not wearing safety glasses shouldwatch from a safe distance. Results: Errors accounted for: Parallax Error:0.
05m Stopwatch/Timing Error: 0.1s Mass measurement error: 0.1g Recordedmeasurements (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 massof combined body after collision: To determine velocity of combined body aftercollision: s = 0.
50m 0.05 t = 1.14s 0.
1 s = 0.50m 10% t = 1.14 8.7% To determinevelocity of ball bearing in barrel of missile launcher: The muzzle velocity ofthis ball bearing gun is: . Errors not incorporated into method: The ballbeating itself has a small drag coefficient, although the cart, which the ballbearing is fired into, may experience air friction. All airfriction/resistance was neglected. Conclusion: This experiment proved myhypothesis correct.
Throughout the entire experiment the overall change inmomentum equaled zero. When the two particles collided there momentum wasconserved resulting in one body that was the combined mass and momentum of theprevious bodies. The result was obtained by recognizing that the initialvelocity/momentum of the ball bearing could be determined by utilizing theconservation of momentum law; that as long as the net resultant external forcesequal zero, the momentum will be constant. From this exercise I learnt newmethod and techniques used in calculating errors and uncertainty.Physics