Question: How would your energy graphs look differently if the mass was 1 kg instead of 0.5 kg? My Response: If the mass of the object was 1 kg instead of 0.5 kg there are definite changes that take place. The potential energy formula which is mass x gravity x height proves that potential energy will increase if mass increases. The gravity and height of the object are still constant, but when the mass of the object doubles from 0.5 kg to 1 kg, this leads to potential energy doubling. When potential energy increases, the potential energy vs. time graph will also be altered. The potential energy graph will be steeper and results in a faster rate of change and the increments on the y axis will be doubled because with a heavier weight, the object will have twice the amount of potential energy as it did before.
Kinetic energy also increases when the mass of the object increases. The formula for kinetic energy is 1/2 x mass x velocity squared. Assuming that velocity is kept constant and that the mass of the object doubled, then the kinetic energy should also increase. The kinetic energy graph will become more steeper. The maximum height the object can reach will increase and contrastingly the minimum height the object can reach will decrease. Due to both the kinetic and potential energy increasing, the total mechincal energy, which is kinetic energy + potential energy, will also increase resulting in a steeper graph.