Question

1. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.2. Inspect your gravitational potential energy vs. time graph for the free-fall flight of the ball. Explain its shape.3. Inspect your Total energy vs. time graph for the free-fall flight of the ball. Explain its shape.4. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? Does the total energy remain constant? Should the total energy remain constant? Why? If it does not, what sources of extra energy are there or where could the missing energy have gone?

Answer 1

1. The kinetic energy vs. time graph for the toss of the ball is expected to be parabolic, initially increasing as the ball gains speed, reaching a maximum at the peak of its trajectory, and then decreasing as it slows down upon descent.
2. The gravitational potential energy vs. time graph for the free-fall flight of the ball is expected to be a decreasing straight line, as the potential energy is converted to kinetic energy during descent.
3. The Total energy vs. time graph for the free-fall flight of the ball is expected to remain constant, forming a horizontal line. This is because the total mechanical energy (kinetic energy + potential energy) should be conserved in the absence of non-conservative forces like air resistance.

Step-by-step explanation:

The shape of the kinetic energy vs. time graph reflects the interplay between kinetic energy and time during the toss. Initially, as the ball is thrown upwards, its kinetic energy increases with the square of its velocity, creating a parabolic curve. At the peak of its trajectory, the kinetic energy is maximized, and upon descent, it decreases as the ball loses speed.

The gravitational potential energy vs. time graph during free fall follows a decreasing straight line. As the ball ascends, potential energy increases linearly with height, reaching its maximum at the peak. During descent, potential energy is converted back into kinetic energy, leading to a linear decrease in potential energy.

The Total energy vs. time graph is expected to be a flat, horizontal line. This represents the conservation of mechanical energy, where the sum of kinetic and potential energy remains constant in the absence of external forces. In ideal conditions without air resistance or other forms of energy dissipation, the total energy of the ball should remain constant throughout its motion.

In conclusion, the graphs provide a visual representation of the principles of energy conservation during the ball's motion. The constant Total energy graph indicates a lack of external energy sources or losses, aligning with the expectation of conservation in an idealized scenario.

Any deviations from this ideal behavior might suggest the presence of non-conservative forces or energy dissipation mechanisms. Understanding these graphs is crucial for analyzing the dynamics of objects in free fall and verifying the principles of energy conservation.

Answer 2

The kinetic energy vs. time graph will fluctuate, while the potential energy vs. time graph will generally have an inverse relationship with it. The total energy vs. time graph should remain constant if there is no energy loss due to external factors. The shape and behavior of these graphs reflect the conservation of mechanical energy in the absence of non-conservative forces.

Step-by-step explanation:

The kinetic energy vs. time graph for a tossed ball would typically show kinetic energy increasing as the ball picks up speed after being thrown, reaching a peak when the ball's speed is greatest, and then decreasing as the ball slows down on its upward path and speeds up again during the descent. The kinetic energy will be the least at the apex of the throw when the velocity is momentarily zero.

The gravitational potential energy vs. time graph for a free-falling ball would increase as the ball rises and reaches the highest point of its flight, where it has the most gravitational potential energy. It would decrease as the ball falls back down, converting potential energy back to kinetic energy.

The Total energy vs. time graph for the free-fall flight of the ball (assuming no air resistance) would show that the total energy remains constant over time since mechanical energy is conserved. This means that total energy, the sum of kinetic and potential energy, is consistent despite the transformation between the two types of energy.

From the total energy graph, we can conclude that the total energy of the ball remains constant during its free-fall motion if there is no energy loss due to external factors such as air resistance or non-conservative forces. If the total energy is not constant, it would imply there are sources of energy loss such as air resistance or thermal energy due to friction.

As for the scenario depicted in an incline experiment, where a marble rolls down from different heights, plotting velocity squared versus the distance traveled by the marble on a level surface results in a straight line illustrating that the marble's kinetic energy at the bottom of the incline is proportional to its height at release point, showing the energy transformation from potential to kinetic energy.

In summary, when analyzing energy graphs or conducting energy experiments, it's essential to understand the conversion between potential and kinetic energy, and consider factors that might affect the total energy of a system.