Lab partner's name:
TA’s name:
Section no
Objective:
Purpose of this experiment was to perceive that momentum is always conserved in absence of net external force acting on the system as well as energy is conserved only sometimes in different collisions.
Data:
Experimental data and parameters calculated from the experimental data have been put in Table -1. The entire table has not fitted in this paper due to large number of columns. So, data in last two parts of the table should be read in conjunction with the data of first part of the table.
Data analysis
Part 1. Calibration
For reading of C3-T2 in the Table -1,
Velocity ratio = (V2-f - V1-f )/( V2-i - V1-i) = (0.576 - 0)/(0 - .587) = 0.98
Momentum calculation:
Initial Momentum = P1-i = M1 x V1-i = 0.266 x 0.587 = 0.156
and P2-i = M2 x V2-i = 0.266 x 0 = 0
Total P before collision = 0.156 +0 = 0.156
Final Momentum = P1-f = M1 x V1-f = 0.266 x 0 = 0
and P2-f = M2 x V2-f = 0.266 x 0.576 = 0.1532
Total P after collision = 0 + 0.1532 = 0.1532
Kinetic energy calculation:
Before collision -
Kinetic energy = 0.5 x M1 xV1-i ^2 = 0.5 x 0.266 x 0.587^2 = 0.045
and 0.5 x M2 x V2-i ^2 = 0.5 x 0.266 x 0 = 0
Total kinetic energy = 0.045
After collision -
Kinetic energy = 0.5 x M2 xV1-f^2 = 0.5 x 0.266 x 0 = 0
and 0.5 x M2 x V2-f ^2 = 0.5 x 0.266 x 0.576 = 0.044
Total kinetic energy = 0.044
ΔP = (0.1532 -0.156)/0.156 = -0.018
ΔP/Pi = 0.018/0.156 = 0.1154 = 11.54%
ΔKE = (0.044 -0.0458)/0.0458 = -0.037
ΔKE/KE = 0.037/0.0458 = 0.807 = 80.7%
Calculation for relative velocity:
For collision #3,
C3-T1:
V1f = (M1-M2).Vi1/(M1+M2) = (0.266-0.266)0.73 /(0.266+0.266) = 0
V2f = (2M1).Vi1/(M1+M2) = (2x0.266)x0.73 /(0.266+0.266) = 0.73
C3-T2:
V1f = (M1-M2).Vi1/(M1+M2) = (0.266-0.266)0.587 /(0.266+0.266) = 0
V2f = (2M1).Vi1/(M1+M2) = (2x0.266)x0.587 /(0.266+0.266) = 0.587
For collision #4,
C4-T1:
V1f = (M1-M2).Vi1/(M1+M2) = (0.266-0.516)0.676 /(0.266+0.516) = 0.216
V2f = (2M1).Vi1/(M1+M2) = (2x0.266)x0.676/(0.266+0.516) = 0.46
C4-T2:
V1f = (M1-M2).Vi1/(M1+M2) = (0.266-0.516)0.58 /(0.266+0.516) = 0.1854
V2f = (2M1).Vi1/(M1+M2) = (2x0.266)x0.58 /(0.266+0.516) = 0.4
For run #4:
C4-T1:
Experimental ratio, r = V1f/ V2f = 0.216/0.46 = 0.47
C4-T2:
Experimental ratio, r = V1f/ V2f = 0.185/0.4 = 0.47
Result
In Part 1 of the experiment, ratios of velocity have been found almost 1 which is the theoretical value of ratio of velocity. Range of the ratios of velocity found is 0.943 to 0.981.
Second part of the experiment is the main part. In this part of the experiment the relative velocity ratio has been found as 0.47. Vi2 is zero, so it can be said that the collision is inelastic one. Here total kinetic energy after collision and kinetic energy before collision are not same. So energy have not conserved in this case. The values of Δ KE/ KEi and Δ P/Pi have been tabulated in following table and data in this table are based on Table- 1.
Discussion and Conclusion
In first part of the experiment ratio of velocity has been found the one as per theoretical value. Slight difference from the theoretical value or error may occur due to friction, tilted track etc. If these kinds of sources of errors are eradicated and experiment can be done more carefully, probability of getting desired result will be higher.
V i.e. velocity was measured in this experiment and there may be error in measuring the velocity. In expression of P = M.V, there is one V. In expression of KE= 0.5M.V^2, there are two Vs. For this reason, we allow the values of ΔP/ Pi to be less than 10% and ΔKE/ KEi to be less than 20% to say whether or not momentum or kinetic energy is conserved.
In the conclusion it can be said that the experiment was carried out safely. By performing this experiment it was understood that momentum is always conserved in absence of net external force acting on the system as well as energy is conserved only sometimes in different collisions.
So, the object of the experiment was met and here lies the success of this lab experiment.
