Lab 4 Report

LAB 4: COLLISIONS Texas A&M University College Station, TX 77843, US. Abstract In this lab, two pucks and tracking software are used to analyze collisions at different angles and to calculate momentum and kinetic energy before and after each collision. Based on the data, most of these collisions did not conserve momentum and lost kinetic energy, indicating that they are inelastic. However, high error values for kinetic energy make it difficult to precisely determine if the collisions are elastic or inelastic. Keywords: momentum, kinetic energy, collision 1. Introduction The goal of this lab is to determine the momentum of the system in the x and y dimension before and after a collision at different angles. The kinetic energy of the system before and after the collision is also calculated to determine if the collisions are elastic or inelastic. Finally, the ratio of momentum before and after the collision is calculated for the x and y dimensions. These exercises will teach students about the effect that differing collision angles have on momentum and the conservation of energy in elastic collisions. | ^ A | = √ A x 2 + A y 2 Equation 1 where | ^ A | is the magnitude of vector A and A x ∧ A y are the vector components σ = √ 1 n − 1 ∑ i = 0 n ( x i −´ x ) 2 Equation 2 where σ is the standard deviation, ´ x is the average of all measurements, and n is the number of measurements δ ´ x = σ n Equation 3 where δ ´ x is the uncertainty, σ is the standard deviation, and n is the number of measurements δf = √ ∂f ∂a δa + ∂f ∂b δb + ∂f ∂c δc … Equation 4 where δf is the propagated error of f where f = f ( a, b, c …), ∂f ∂a is the partial derivative with respect to variable a , and δa is the uncertainty associated with a ´ r 1 · ´ r 2 | ´ r 1 || ´ r 2 | θ = acos ¿ ) Equation 5 where θ is the angle between two vectors and ´ r is a vector p = mv Equation 6 where p is momentum, m is mass, and v is velocity K = 1 2 mv 2 Equation 7 where K is kinetic energy, m is mass, and v is velocity 2. Experimental Procedure Before any measurements could be made with the tracking program, the conversion factor from pixels to cm had to be entered into the program. The distance from the camera to the table top was measured and entered into the program so that the program would automatically convert from pixels to cm. Two pucks with different colored tracking stickers were used for the collision trials, and the air table was turned on to give an almost frictionless surface. The pucks were pushed towards each other at 8 different angles: 90°, 180°, three angles between 90 and