Question

In this experiment you will apply your knowledge of Conservation of Energy to a given data set. Table 5 contains data for the position of a ball with mass 0.5 kg that has been dropped from 5 meters from rest at given time points. In order to test the conservation of energy, the potential energy and kinetic energy of the ball need to be calculated.

Please help me fill in the rest of the values for the table (and understand how to do them). Thank you!

Time (s)	Ball Position (m)	Ball Velocity (m/s)	Potential Energy (J)	Kinetic Energy (J)	Total Energy (J)
0.00	5.00
0.05	4.99	-.40
0.10	4.96	-1.00
0.15	4.89	-1.80
0.20	4.78	-2.0
0.25	4.69	-2.40
0.30	4.54	-2.90
0.35	4.40	-3.20
0.40	4.22	-4.00
0.45	4.00	-4.20
0.50	3.80	-5.00
0.55	3.50	-5.40
0.60	3.26	-5.70
0.65	2.93	-6.60
0.70	2.60	-7.00
0.75	2.23	-7.20
0.80	1.88	-7.70
0.85	1.46	-8.30
0.90	1.05	-8.80
0.95	0.58	-9-9.40
1.00	0.11

Answer 1

Time	Ball Position (m)	Ball velocity (m/s)	Potential energy (J)	Kinetic Energy (J)	Toatal Energy (J)
0.00	5.00
0.05	4.99	-0.40	24.48	0.04	24.52
0.10	4.96	-1.00	24.33	0.25	24.58
0.15	4.89	-1.80	23.99	0.81	24.80
0.20	4.78	-2.0	23.45	1.00	24.45
0.25	4.69	-2.40	23.00	1.44	24.44
0.30	4.54	-2.90	22.27	2.10	24.37
0.35	4.40	-3.20	21.58	2.56	24.14
0.40	4.22	-4.00	20.70	4.00	24.70
0.45	4.00	-4.20	19.62	4.41	24.03
0.50	3.80	-5.00	18.64	6.25	24.89

Rest part of the table, you can fill up. This is not a tough problem only mathematical calculation is needed.

The potential energy is calcualted using the expression, PE = m*g*h

given that, m = 0.50, g = 9.81 m/s², and the value of h is substituted as 4.99, 4.96, 4.89 and so on.

Like-wise, Kinetic energy is calculated using the expression, KE = (1/2)*m*v²

here, v can be substituted as 0.40, 1.00, 1.80 and so on.

Total energy is the sum of these two energies.