To answer the questions based on gravitational potential energy (GPE) and energy transformations:
A) How much gravitational potential energy (GPE) does the ball have at point A?
The formula for gravitational potential energy is given by:
\[ \text{GPE} = \text{weight} \times \text{height} \]
Assuming point A corresponds to the height at which the ball is held before dropping, you would need the height at point A to calculate the GPE. If we assume that the ball is at a height \( h \) (in meters), then the GPE at point A would be:
\[ \text{GPE} = 2 , \text{N} \times h , \text{m} = 2h , \text{J} \]
Without the specific height value at point A, we can't give a numeric answer. However, you can plug in the actual height measurement from the graph to find the exact GPE in joules.
B) Explain what happens to this energy as the ball bounces from point A to B to C.
As the ball bounces from point A to B to C, the gravitational potential energy (GPE) is converted into kinetic energy (KE) and back during the ball's motion.
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At point A (Before the drop): The ball has maximum GPE because it is at its highest point. The GPE is at its highest while the kinetic energy is at its minimum (0 J if it is held stationary).
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As the ball descends to point B: The GPE decreases as the height decreases. This lost GPE is converted into kinetic energy, causing the ball to accelerate and gain speed as it descends.
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At point B (Lowest point of the bounce): Here, the ball has its maximum kinetic energy because it is moving at its fastest speed. The gravitational potential energy is at its minimum, having been converted almost entirely into kinetic energy.
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As the ball bounces back up to point C: The kinetic energy starts to convert back into gravitational potential energy as it rises again. As the ball moves upward towards point C, its speed decreases (losing kinetic energy) while its height increases (gaining GPE).
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At point C: The GPE increases again as the ball reaches a height. Ideally, if no energy is lost to air resistance or other forms of friction, the ball would rise to the same height it was dropped from (point A), restoring its GPE.
Throughout the bouncing process, the total mechanical energy of the system (considering GPE and KE) remains roughly conserved if no external forces (like air resistance) do significant work against the ball. However, in practice, some energy may be lost to sound, heat, or deformation of the ball and the surface on impact, resulting in lower bounce heights over time.
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