Embedded Files
Alison Whitney November 10, 2023
Group Members: Rook Bergeron, Nick Tinglof
Background: Collisions occur when two objects transfer energy between each other through physical contact. We experience them in our every day lives as we bump into an object and knock it over, fall off our skateboards, or witness a minor car accident. There are three primary types of collisions; elastic, inelastic, and perfectly inelastic. Each collision type has a different relationship with energy transfer as well. Elastic collisions occur when two objects bump into each other and bounce right off with no deformation of their physical form. This type of collision experiences both a conservation of momentum and a conservation of kinetic energy as minimal energy is lost to physical damage. One example is throwing a bouncy ball on the floor. It collides with the floor and bounces back upwards with no change in its physical shape and no damage to the floor itself. Inelastic collisions occur when two objects bump into eachother and there is a deformation in one or both of their physical forms. This collision type experiences the conservation of momentum, but not the conservation of kinetic energy as energy will be lost from the system as a result of the damage. For example, a minor car accident in which the two cars collide and bounce off of each other, but now both of their bumpers are squished. Perfectly inelastic collisions occur when two objects collide in such a way that they become a single object. Similarly to inelastic collisions, perfectly inelastic collisions experience the conservation of momentum but not the conservation of kinetic energy. For example, when train cars are coupled together they are pushed into each other and the collision engages the locking mechanism. The train cars are then locked together and become one. A special type of inelastic collision can also occur in which one object splits off into multiple, such as a firework exploding into many independent pieces.
This experiment intended to explore elastic and perfectly inelastic collisions utilizing small cars. The velocities of the cars were monitored using tracking sensors as the cars were collided together first in an elastic collision and then in a perfectly inelastic collision as tape was used to hold them together as one object. The velocities of each car were then used to track the conservation of momentum and conservation of kinetic energy of each collision type to monitor if they followed the expected patterns.
Methods:
Elastic Collision:
Two GoDirect Motion sensors were set up on opposite sites of a plastic ramp facing inwards.
The masses of two small plastic cars was measured with a digital scale.
One of the cars was placed at about the halfway point on the ramp.
The second car was positioned at the end of the ramp, a few centimeters from the sensor.
The second car was given a push towards the first car and allowed to collide and bounce back off.
The velocity graph produced by the sensors was used to determine the approximate velocity of the cars directly before and after the collision.
The measurements were plugged into the elastic conservation of momentum equation to determine if momentum was conserved.
Perfectly Inelastic Collision:
Two GoDirect Motion sensors were set up on opposite sites of a plastic ramp facing inwards.
The masses of two small plastic cars was measured with a digital scale.
Masking tape was added to the front of each car with the sticky side facing outwards.
One of the cars was placed at about the halfway point on the ramp.
The second car was positioned at the end of the ramp, a few centimeters from the sensor.
The second car was given a push towards the first car and allowed to collide so that the tape made the cars stick together after the collision.
The velocity graph produced by the sensors was used to determine the approximate velocity of the cars directly before and after the collision.
The measurements were plugged into the perfectly inelastic conservation of momentum equation to determine if momentum was conserved.
The Go Direct Motion sensor
The Go Direct Motion sensor
The experimental ramp set up with both cars
The experimental ramp set up with both cars
A video of the elastic collision
A video of the elastic collision
Equations:
Elastic Conservation of Momentum:
m1v1o + m2v2o = m1v1f +m2v2f
Elastic Conservation of Kinetic Energy:
1/2 m1v1o^2 + 1/2 m2v2o^2 = 1/2 m1v1f^2 + 1/2 m2v2f^2
Perfectly Inelastic Conservation of Momentum:
m1v1o + m2v2o = (m1+m2)vf
Raw Data:
Elastic Collision:
Mass of Car 1 = 0.222 kg Mass of Car 2 = 0.223 kg
Initial Velocity of Car 1 = 0.238 m/s Initial Velocity of Car 2 = 0 m/s
Final Velocity of Car 1 = 0.059 m/s Final Velocity of Car 2 = 0.142 m/s
Perfectly Inelastic Collision:
Mass of Car 1 = 0.222 kg Mass of Car 2 = 0.223 kg
Initial Velocity of Car 1 = 0.239 m/s Initial Velocity of Car 2 = 0 m/s
Final Velocity of Car 1 and Car 2 = 0.235 m/s
The figure produced by the sensors for the elastic collision
The figure produced by the sensors for the elastic collision
The red line represents the velocity of car 1 while the blue line represents the velocity of car 2. The two lines on top illustrate the position versus time measurements of both cars.
The figure produced by the sensors for the perfectly inelastic collision
The figure produced by the sensors for the perfectly inelastic collision
The red line represents the velocity of car 1 while the blue line represents the velocity of car 2. The two lines on top illustrate the position versus time measurements of both cars.
Results:
The conservation of momentum equation for the elastic collision resulted in 0.0528 = 0.0448, so momentum was not shown to be conserved through the collision. The conservation of kinetic energy equation for the elastic collision resulted in 0.00629 = 0.00263, and the almost three-fold difference between the results meant that kinetic energy was also not conserved. When examining the perfectly inelastic collision, momentum was observed to not be conserved as the equation resulted in 0.0531 = 0.105.
Discussion: This results of the experiment suggested that the two cars did not follow any of the expected trends when they experienced an elastic and a perfectly inelastic collision with each other. In elastic collisions, it is known that both momentum and kinetic energy will be conserved, but the results found that both were not conserved. Similarly, in perfectly inelastic collisions the momentum should be conserved even though the results suggested the opposite. These skewed results were likely caused by a combination outside factors that were not able to be accounted for. The first being that this was a real-world experiment instead of a hypothetical situation, so some energy would be lost in noise and other non-conserved variables that were not able to be measured and accounted for. It was also probable that there was a combination of equipment error and human error in the measurements as this was the first time that the GoDirect Motion sensors were used by the participants in the experiment and the readings included many extraneous peaks that did not align with the observed velocities of the cars.
Future experiments could attempt this study again using a variety of different techniques to measure the velocity of the cars to determine which method results in the least human and equipment errors. Other experiments could attempt to estimate the amount of energy that is lost from the system through the noise of the collision.
Error: There was substantial room for errors in this experiment including the standard expected errors as a result of conducting the trials in a real-world setting. In addition to those small human errors however, this experiment relied on a program and sensors that had not been used previously by any of the participants. This meant that there were many errors made as the program was learned. It was observed that the program had some difficulty in accurately tracking the velocities of each car as well. As trials were repeated there were drastically different results despite being under the same conditions, as well as many peaks and measured changes in velocity that did not occur in the movement of the cars. Ultimately, the cleanest measurements with the least extraneous peaks were selected to provide the results for the study, but it is still possible that there was some equipment error in the measurements as well.
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