M3.4 Laboratory Report 6

M3.4 Laboratory 6 Worksheet 10/8/2023 PHY2053L Purpose: The purpose of this experiment is to investigate the principles of conservation of momentum and kinetic energy in various types of collisions, both one-dimensional and two-dimensional. By conducting this experiment, I

aim to explore the behavior of objects during elastic and inelastic collisions, understand how different factors, such as mass and velocity, affect the outcomes of collisions, and calculate and analyze the ratios of final kinetic energy to initial kinetic energy and final momentum to initial momentum for different collision scenarios. Introduction: The key principles to be explored in this experiment are the conservation of momentum and the conservation of kinetic energy. These principles are fundamental in physics and are essential for understanding how objects interact ins a closed system. Procedure: Part l: One Dimensional Collisions Part 1.1: Elastic Collision 1- Use the mass controller to control the mass of the balls (m 1 and m 2 ). 2- Control the balls velocity by changing the length and the direction of the velocity vector. (press on the circle at the tip of the velocity vector and then drag to change its magnitude and direction). 3- For elastic collision use the elasticity controller (drag the Elasticity Slider) to choose the collision type (elastic for this part). 4- Once you fix your variables, select More Data to record your data before collision and then press play. After the two balls collide, pause the simulation to record your data after collision. 5- Fill tables 1(a), Table 1(b) and Table 1(c). Part 1.2: Inelastic Collision 1- Use the mass controller to control the mass of the balls (m 1 and m 2 ). 2- Control the balls velocity by changing the length and the direction of the velocity vector. (press on the circle at the tip of the velocity vector, and then drag to change its magnitude and direction). 3- For inelastic collision use the elasticity controller (drag the blue triangle to the left) to choose the collision type (inelastic for this part). 4- Once you fix your variables, select More Data to record your data before collision and then press play. After the two balls collide, pause the simulation to record your data after collision.

0.64 0.00 0.00 0.64 1.72 0.00 0.00 1.72 K 1 /K f = 1.34/1.34 Table 1(b): V 1i (m/s) V 2i (m/s) V 1f (m/s) V 2f (m/s) P 1i (kgm/s) P 2i (kg.m/s) P 1f (kg.m/s) P 2f (kg.m/s) 1.00 0.00 -0.14 0.86 1.73 0.00 -0.24 1.97 1.00 0.00 -0.20 0.80 2.00 0.00 -0.40 2.40 Table 1(c): V 1i (m/s) V 2i (m/s) V 1f (m/s) V 2f (m/s) P 1i (kgm/s) P 2i (kg.m/s) P 1f (kg.m/s) P 2f (kg.m/s) 1.00 -1.00 -1.62 0.38 1.46 -2.77 -2.36 1.05 P i (kg.m/s) P f (kg.m/s) K i (J) K i1 + K i2 K f (J) K f1 + K f2 2.68 2.68 1.34 1.34 1.72 1.72 0.55 0.55 P i (kg.m/s) P f (kg.m/s) K i (J) K i1 + K i2 K f (J) K f1 + K f2 1.73 1.73 0.87 0.86 2.00 2.00 1.00 1.00

0.80 -0.80 -1.30 0.30 1.17 -2.22 -1.89 0.84 Part 1.2: Inelastic Collision Table 2(a): V 1i (m/s) V 2i (m/s) V 1f (m/s) V 2f (m/s) P 1i (kgm/s) P 2i (kg.m/s) P 1f (kg.m/s) P 2f (kg.m/s) 1.00 0.00 0.42 0.42 2.12 0.00 0.90 1.22 0.70 0.00 0.30 0.30 1.48 0.00 0.63 0.85 Table 2(b): V 1i (m/s) V 2i (m/s) V 1f (m/s) V 2f (m/s) P 1i (kgm/s) P 2i (kg.m/s) P 1f (kg.m/s) P 2f (kg.m/s) 0.70 -0.70 -0.11 -0.11 1.48 -2.01 -0.22 -0.30 1.00 -1.00 -0.15 -0.15 2.12 -2.87 -0.32 -0.43 P i (kg.m/s) P f (kg.m/s) K i (J) K i1 + K i2 K f (J) K f1 + K f2 -1.31 -1.31 2.12 2.22 -1.05 -1.05 1.35 1.35 P i (kg.m/s) P f (kg.m/s) K i (J) K i1 + K i2 K f (J) K f1 + K f2 2.12 2.12 1.06 0.45 1.48 1.48 0.52 0.22 P i (kg.m/s) P f (kg.m/s) K i (J) K i1 + K i2 K f (J) K f1 + K f2 -0.53 -0.52 1.22 0.03 -0.75 -0.75 2.50 0.06

Table 3(b): V 1xi (m/s ) V 2xi (m/s ) V 1xf (m/s ) V 2xf (m/s ) P 1xi (kg.m/s) P 2xi (kg.m/s) P 1xf (kg.m/s) P 2xf (kg.m/s) P xi (kg.m/s) P xf (kg.m/s) 0.99 -0.85 -0.12 -0.30 2.10 -2.44 -0.25 -0.09 -0.34 -0.34 0.80 -0.67 -0.08 -0.02 1.70 -1.92 -0.17 -0.06 -0.22 -0.23 V 1yi (m/s ) V 2yi (m/s ) V 1yf (m/s ) V 2yf (m/s ) P 1yi (kg.m/s) P 2yi (kg.m/s) P 1yf (kg.m/s) P 2yf (kg.m/s) P yi (kg.m/s) P yf (kg.m/s) 0.16 -0.52 0.17 -0.52 0.34 -1.49 0.35 -1.50 -1.15 -1.15 0.09 -0.46 0.11 -0.48 0.19 -1.32 0.23 -1.36 -1.13 -1.13 P i (kg.m/s) K i (J) P f (kg.m/s) K f (J) -1.49 2.49 -1.49 2.49 -1.35 1.63 -1.36 0.34 Conclusion: In summary, my observations reveal that in one-dimensional elastic collisions, the conservation of both kinetic energy and momentum remained consistent when the masses of the objects involved were unaltered. Similarly, even when the masses were varied in one-dimensional elastic collisions, both kinetic energy and momentum were conserved. However, something notable from this pattern was observed in the case of inelastic collisions. In both one-dimensional and two-dimensional scenarios, it

was evident that kinetic energy was not conserved, with the final kinetic energy being significantly lower than the initial kinetic energy.