balastics

CONCEPTUAL QUESTIONS BALLISTICS WORKSHEET PS 113L – Intro Physics I Laboratory / 50pts Name: Noah Courtney Section # : 1. During the entire firing sequence for the ballistic pendulum experiment there are four distinct states that the system progresses through: (1) spring compressed and all components stationary; (2) spring fired, ball traveling at v1, pendulum stationary; (3) ball and pendulum traveling together at v2 just after collision, (4) ball and pendulum stationary at some height Δh. So there are 3 transitions between these 4 states when energy and momentum might be conserved. Below, indicate for each transition whether energy or momentum is conserved, and briefly write your reasoning for your determination. Transition Mechanical Energy Conserved? (Yes,No) Momentum Conserved? (Yes,No) Explain your Choices (1)  (2) Yes No The spring gave a net force that was not balanced (2)  (3) No Yes No net external forces (3)  (4) Yes No No external forces acting upon it. Kinetic energy converted to gravitational potential. 2. The lab manual derived an equation to determine the projectile velocity if we fired it into a ballistic pendulum assuming the simplest approach (measuring change in height): 𝑣? ? ⃑ 1 = ?? + 𝑀𝑀 � 2 ?? ∆ ℎ ?? However, mechanically the simplest way is to measure the max angle the pendulum swings up to. Knowing the geometry, you can derive a substitution using trigonometry. Show how you would derive the substitution: ∆ ℎ = ?? 𝐶𝐶 𝑀𝑀 (1 − cos ?? ) Page 1

Pendulum Mass, M = .246 ± .5_ Projectile Mass, m = .066 ± .5 _ Pendulum Length, R CM = .3 ± .05_ m Trial # Swing Angle (degrees) Projectile Velocity, v 1 (m/s) 1 29.5 4.13 2 25.5 3.58 3 27 3.78 4 28.5 3.99 5 23.5 3.3 6 22 3.13 7 19.5 2.98 *Assume g = 9.7926 m/s 2 Method 1 Mean Projectile Velocity, 𝒗𝒗 � 𝟏𝟏 = 3.756 ± 33 _ m/s *Note the ± uncertainty here is your calculated standard deviation: ?? 𝑣𝑣 1 . 3. Review your data. Think about how you performed this method as well as any assumptions used when applying our theoretical physics equations to our setup and equipment. What kinds of uncertainties may have influenced your result and contributed to the variation between trials? Air resistance against ball, the friction between the ball and the cylinder walls, the momentum of the angle measure, and the air resistance on the pendulum itself PART 1: VELOCITY DETERMINATION FROM BALLISTIC PENDULUM Page 2

Method 1 (Pendulum) Mean Projectile Velocity, 𝒗𝒗 � 𝟏𝟏 = ± _ m/s Method 2 (Range) Mean Projectile Velocity, 𝒗𝒗 � 𝟏 𝟏 ′ = ± _ m/s 8. What is the Percent Difference between the velocities of your two methods? % 𝐷𝐷𝐷𝐷 𝐷𝐷𝐷𝐷 = 0.42% Agreement Between Methods, Determination of Success/Failure � 𝑣? ? � 1 − 𝑣? ? � ′ � ?? 𝑣𝑣?? ( 𝑣? ? � 1 , 𝑣? ? � ′ ) ∗ 100% Calculate the following quantities Discrepancy between the two velocity methods: 𝑑𝑑 = 𝑣 𝑣 1 0.016 − 𝑣𝑣 ̅ ′ Uncertainty in the discrepancy between methods: ?? 𝑑𝑑 = � ? ? 𝑣? ? � 1 2 + ?? ′ 2 0.34 □ If 𝑑𝑑 ≤ 1 . 96 ?? 𝑑𝑑 , then our methods agree within our experimental uncertainties and we successfully found the velocity of the projectile by two independent methods. □ If 𝑑𝑑 > 1 . 96 ?? 𝑑𝑑 , then our methods disagree above our experimental uncertainties and our results for determining projectile velocity are inconclusive. If it is close to the cutoff point. □ If 𝑑𝑑 ≫ 1 . 96 ?? 𝑑𝑑 , then our methods greatly disagree given our experimental uncertainties. This discrepancy is highly significant and either the theory, methods, or measurements need to be checked for mistakes Much greater than the cutoff point. 9. Explain which method you believe gives the more consistent result. Which method do you believe gives the more true result? The first one is more true while the second is more consentient. This is probably because of more variables to create errors in the data. Thoughts for Improvement 10. Thinking back on how you conducted the experiment and analysis, would you perform it the same or would you do something different? Try to come up with at least 1 practical, non-trivial improvement you would make. Describe why you think this would improve the experiment and better meet its objectives. Improving precision and accuracy would be most effective way to improve the results of the experiment. Also having more reliable equipment may also help us better in obtaining the information needed. COMPARISON BETWEEN VELOCITY DETERMINATION METHODS Page 4 1 1 ? 𝑣 ? ? 1