TA’s Name
Objective of Section
The experiment was aimed at investigating collision in two dimensions. The study sort to check whether the recorded energy after the collision is equal to the theoretical figure as well as calculating the discrepancy realized.
Experimental Data
Data Analysis
In two dimension collision, the momentum and kinetic energy before and after collision should be equal. The law of conservation of energy stipulates that the energy before and after collision should be equal, especially if there was no lost energy. However, in reality, some energy is converted into other forms of energy, hence the momentum of the pucks may before and after collision may not be the same. In a two dimension collision, the vector sum of different initial momenta of the two balls should be equal to the vector sum of the momenta or kinetic energies of the balls after the collision if the collision was purely elastic. However, most macroscopic collisions are inelastic and some energy is lost through conversion into other forms.
For two dimension collisions, the equation of conservation of momentum is adjusted as follows:
m1v 1ix + m2v 2ix = m1 v1fx + m2 v2fx
m1v 1iy + m2v 2iy = m1 v1fy + m2 v2fy
The equations depict that the momentum in the x- and y-axis is equal before and after collision. The total initial momentum can, therefore, be calculated by adding up the x and the y components of the two pucks before the collision. In the same way, the final momentum is the sum total of the x and y components of both pucks after the collision.
In determining the kinetic energy of the pucks, it is important to note that the pucks may have both linear and rotational motions. As such, the calculation of kinetic energy should take into account the two types of motions and the resultant kinetic energy. The formula used for the calculation is as below:
½ m1v2 1i + ½ m2v2 2i + ½ I1 ω21i + ½ I2 ω22i= ½ m1 v21f + ½ m2 v22f +½ I2 ω21f + ½ I2 ω22f
The rotational kinetic energy of the two pucks before and after collisions is expected to be equal in tandem with the law of conservation of energy. However, there are some discrepancies that occur due to errors as well as conversion of energy into other forms.
Calculate Pf and discrepancy
In calculating the final momentum of the pucks, it is important to know the final momentum of the pucks both in x and y-axis.
The x-component of the momentum of the red puck is,
Pxf= m1 v1fx
M1=0.05kg
V1fx=0.02365 m/s
Therefore Pxf=0.05kg x 0.02365 m/s
=0.0011825 kg m/s
For the y-component for the red puck is,
Pyf= m1 v1fy
M1=0.05kg
V1fy=0.2466 m/s
Therefore Pxf=0.05kg x 0.2466m/s
=0.01233 kg m/s
For the x-component for the blue puck is,
Pxf2= m2 v2fx
M2=0.05kg
V2fx=0 m/s
Therefore Pxf2=0.05kg x 0 m/sm/s
=0 kg m/s
For the y-component for the blue puck is,
Pyf= m2 v2fy
M1=0.05kg
V2fy=0.0 m/s
Therefore Pyf=0.05kg x 0.0m/s
=0.0 kg m/s
Pf = Pxf2 + Pyf =0.01233 kg m/s +0.0011825 kg m/s
= 0.0135125 kg m/s
Results
Discussion and Conclusion
In two dimension collision, the pucks have two types of motion possible for them. There is the rotational motion and the linear motion along the x- or y-axis. The purpose of this experiment was to investigate how collision in two-dimension takes place. The study sort to prove the law of conservation of energy and provide explanation for any discrepancies that may occur. The data was collected as expected with the collision being both elastic and inelastic.
The percent change in kinetic energy in the red pucks was zero while the percent change in blue puck was 40 percent. This shows that the red pucks conserved all the kinetic energy while the blue puck lost some energy. The lost energy could be as a result of conversion into other forms of energy, or due to experimental errors. The linear speed before the collision was found to be 0.144526399 m/s while the resultant linear speed after collision was a bit slower at 0.144428945 m/s for the red puck.
Further, angular velocity for the red puck was slower after the collision. For the blue puck, both linear and angular velocities showed considerable differences hence the high kinetic energy differences recorded for this puck. In addition, inertia was high in blue pucks that it was in red pucks. This resulted to a velocity of zero for the resultant speed for the blue puck after collision. Interestingly, kinetic energy for the blue ball was higher after the collision than before collision. This is only possible in the event of external force acting on the puck after collision, such as force may be from chemical reaction or faulty experimental apparatus.
Discrepancies appeared in the results of the blue puck. The higher records for kinetic energy and momentum after the collision depict discrepancies in the theoretical results. Since there was no chemical explosion, the only other logical conclusion is that there might have been some systemic errors in the apparatus used. The most possible one could be that the mass of the blue puck was not properly measured hence the skewed results. Despite the challenge, the experiment was successful since the students were able to get data from the experiment.
