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 – 65.9 g 0.1, Approx Size – 2 cm in diameter) This will be the projectile that is fired from the missile launcher. One (1) Cart. (Weight – 678.3 g 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 – 0.50 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 0.50 m 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: 0.05 m Stopwatch / Timing Error: 0.1’s Mass measurement error: 0.1 g Recorded measurements (NOT including uncertainty): Times for overall journey: 1.13’s, 1.13’s, and 1.16’s Distance: 0.50 m Mass of Ball Bearing: 65.9 g Mass of Cart: 678.3 g To determine average time (NOT including uncertainty): To determine mass of combined body after collision: To determine velocity of combined body after collision:’s = 0.50 m 0.05 t = 1.14’s 0.1’s = 0.50 m 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.