Lab partner's name:
Purpose of this experiment was to check conservation of energy in three simple mechanical systems namely swinging pendulum, oscillating mass on a spring and basketball shot.
Following is the table of experimental data for Swinging Pendulum system
Following graphs have been obtained from above experimental data.
Graph -1: Kinetic energy vs Vertical Direction
Graph -2: ME.PE,KE vs time
Following is the graph of experimental data for Oscillating spring-mass system
Graph -3: ME.PE,KE vs time
Following is the table of experimental data for Basketball shot
Following graphs were obtained from above experimental data.
Graph -4: ME.PE,KE vs time
Graph-5: Kinetic Energy vs Y
Part 1. Swinging pendulum
For first reading in the Table -1,
Kinetic energy per unit mass (K/m) = 0.5 x (vx2 + vy2) = 0.5x (0.059^2 + 0.049^2) = 0.003 J/kg
Potential energy per unit mass (P/m) = 9.8 x y = 9.8 x 0.1005 = 0.985
Total mechanical energy per unit mass (E/m) = 0.003 +0.985 = 0.988
Now, E = K + m.g.y
or, K/m = E/m – g.y .. (1)
In graph, values of “K/m” were plotted against “y”. From equation no. 1, it can be found out that “–g” is the slope of straight line in the graph.
Part 3. Basketball shot
For first reading in the Table -2,
Kinetic energy (K) = 0.5 x mass of ball x (vx2 + vy2) = 0.5 x 0.62 x (4.29^2 + 3.414^2) = 9.318 J
Potential energy (P) = 9.8 x mass of ball x y = 9.8 x 0.62 x 2.719 = 16.535 J
Total mechanical energy (E) = 9.318 +16.535 = 25.853 J
Now, E = K + m.g.y
or, K = E – mg.y .. (2)
In graph, values of “K/m” were plotted against “y”. From equation no. 2, it can be found out that “–mg” is the slope of straight line in the graph. By dividing value of slope of the graph by the mass of the ball i.e. 0.62 kg , value of “g” were obtained.
so, g = 5.025/0.62 = 8.1 m/s^2
Discussion and Conclusion
According to law of conservation of energy, energy can not be created or destroyed. So, mechanical energy should be constant throughout the experiment. Mechanical energy of first two cases was almost constant, as the slope of the graph of mechanical energy i.e. the straight line has negligible slope. For last case, the graph of mechanical energy had a little slope which was greater than previous two cases and this meant that mechanical energy was not constant throughout the experiment.
Minimum value of pendulum’s gravitational potential energy was zero. The arbitrary reference level that was used to measure the y coordinate was at the lowest point of the swing. If the reference level was moved, value of ME/m would not change as mechanical energy is constant; value of KE/m and PE/m would not change as they are function of Pendulum position whose value depends on length of pendulum and angle.
Basketball had maximum kinetic energy when its position in its motion was at x =5.08 m and y = 0.4605 with respect to coordinate system. Basketball had minimum kinetic energy when its position in its motion was at x =1.641 m and y = 3.465 with respect to coordinate system. Basketball had maximum potential energy when its position in its motion was at x =1.904 m and y = 3.499 with respect to coordinate system. Basketball had minimum potential energy when its position in its motion was at x = 5.08 m and y = 0.4605 with respect to coordinate system. If value of y would be measured from ceiling, the values of y would be changed due to change of position of coordinate system
In conclusion it can be said that the experiments were carried out safely and it was successful as it almost met the objective of the experiment. Though in last experiment total mechanical energy was found not constant throughout the experiment but deviation of the value of the energy from the expected value is not considerably high to prove false the law of conservation of energy. This deviation may be due to improper measurement, committing mistake in taking records, loss of energy due to friction etc. However, by performing this experiment it was perceived that total amount of mechanical energy always remains constant. Energy cannot be created or destroyed and it only transformed into other form of energy. In this experiment, potential energy transformed into kinetic energy and vice versa. But total mechanical energy remained unchanged.