LAB 15 - Collisions in Two Dimensions
Tony Wu, Isaiah Hernandez
October 18, 2016
Experimental Procedure: After setting up the table and the phone, we recorded the collision between the steel ball and the marble. Then we recorded the collision between one marble into a another. We uploaded the slow motion videos onto Logger pro. We marked the position of each ball as we stepped forward every few frames. This gives us an estimate of how fast each ball is moving. We are able to check the speed of each ball before and after the collision, allowing us to determine if momentum and energy are conserved.
Data and Calculations:
(M) Steel Ball Mass: 67.0 g Initial Velocity: 0.1791 m/s Final Velocity: 0.04636 m/s
(m) Marble Mass: 19.7 g Initial Velocity: 0 m/s Final Velocity: 0.1157 m/s
Conservation of Momentum:
M * Vel_M_Final + m * Vel_m_Final - M * Vel_M_Initial - m * Vel_m_inital = 0
0.067 kg (0.04636 m/s) + 0.0197 kg (0.1157 m/s) - 0.067 kg (0.1791 m/s - 19.7 g (0 m/s) = 0
-0.0066 kg*m/s ~= 0 m/s
Conservation of Energy:
1/2 (M*Vel_M_Final^2) + 1/2(m*Vel_m_Final^2) - 1/2 (M*Vel_M_Initial^2) + 1/2(M*Vel_m_Initial^2) = 0
Conclusions:
As you can see from the calculations, momentum and energy are both conserved. The numbers are not exactly equal to zero due to our experiment not being entirely ideal. The error comes from not being able to accurately plot the precise movement of each ball. Another source of error is friction from the table and loss of energy as heat and sound from the collision.
Lab Goal: Look at two-dimensional collisions and determine if momentum and energy are conserved.
Theory/Introduction: In an ideal collision, momentum (P = Mass * Velocity) and energy are conserved. In this experiment we are focusing on kinetic energy (KE = 1/2 * Mass * Velocity Squared), We are testing collisions between two balls. The first test is rolling a steel ball into a marble that is stationary. The second test is rolling a marble into steel ball that is stationary. Each marble has a different mass which affects the final momentum of each. An object that collides with a less massive object would result in not much of a change in the original object, but a large change in momentum of the smaller object.
Apparatus: The apparatus is a glass table with adjustable legs. The glass table is to simulate a frictionless surface, preventing loss of energy due to friction. We had to adjust the legs individually to level the table so that the balls are not rolling on a slope. The long metal stand at the top is to clip a phone in. The phone records the collisions in slow motion.
Theory/Introduction: In an ideal collision, momentum (P = Mass * Velocity) and energy are conserved. In this experiment we are focusing on kinetic energy (KE = 1/2 * Mass * Velocity Squared), We are testing collisions between two balls. The first test is rolling a steel ball into a marble that is stationary. The second test is rolling a marble into steel ball that is stationary. Each marble has a different mass which affects the final momentum of each. An object that collides with a less massive object would result in not much of a change in the original object, but a large change in momentum of the smaller object.
Apparatus: The apparatus is a glass table with adjustable legs. The glass table is to simulate a frictionless surface, preventing loss of energy due to friction. We had to adjust the legs individually to level the table so that the balls are not rolling on a slope. The long metal stand at the top is to clip a phone in. The phone records the collisions in slow motion.
Data and Calculations:
X and Y Values for the Center of Mass
In a controlled system, the center of mass does not change. This is seen in the pink colored line, the center of mass of the two marbles before and after the collision. The center of mass is calculated from the X and Y values of each ball, multiplied by their mass and divided by the sum of the mass of both balls.
Xcm = (M*X1 + m*X2) / (M + m)
Ycm = (M*Y1 + m*Y2) / (M + m)
These calculations are repeated for every data point in order to generate the data points that chart the movement of the center of mass.
The X and Y Velocities of the Center of Mass
This graph is a a lot more scattered because of the inability to perfectly mark the travel path of each ball.
X and Y Position for the Center of Mass of Both Balls
This is a great graph for showing that the center of mass of the balls maintain a straight line course even
after the collision.
X and Y Values before and after the Collision
X and Y are the values for the rolling ball, X2 and Y2 are the values for the ball the stationary ball.
(m) Marble Mass: 19.7 g Initial Velocity: 0 m/s Final Velocity: 0.1157 m/s
Conservation of Momentum:
M * Vel_M_Final + m * Vel_m_Final - M * Vel_M_Initial - m * Vel_m_inital = 0
0.067 kg (0.04636 m/s) + 0.0197 kg (0.1157 m/s) - 0.067 kg (0.1791 m/s - 19.7 g (0 m/s) = 0
-0.0066 kg*m/s ~= 0 m/s
Conservation of Energy:
1/2 (M*Vel_M_Final^2) + 1/2(m*Vel_m_Final^2) - 1/2 (M*Vel_M_Initial^2) + 1/2(M*Vel_m_Initial^2) = 0
1/2 (0.067 kg) (0.04636 m/s)^2 + 1/2 (0.0197 kg) (0.1157 m/s)^2 - 1/2 (0.067 kg) (0.1791 m/s)^2 - 1/2 (0.0197 kg) (0 m/s)^2 = 0
-0.00087 Joule = 0
As you can see from the calculations, momentum and energy are both conserved. The numbers are not exactly equal to zero due to our experiment not being entirely ideal. The error comes from not being able to accurately plot the precise movement of each ball. Another source of error is friction from the table and loss of energy as heat and sound from the collision.
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