If a monkey dropped a banana off of a cliff, where are the potential energy and kinetic energy of the bananas equal.
A at the bottom
B at the top
C a quarter of the way down
D half way down
The potential energy of the banana is at its maximum at the top of the cliff, and it decreases as the banana falls. On the other hand, the kinetic energy of the banana is zero at the top of the cliff because the banana is initially at rest, and it increases as the banana falls due to its increasing velocity.
The potential energy and kinetic energy of the banana are equal when the banana is halfway down the cliff. At this point, the potential energy has decreased by half, and the kinetic energy has increased by half.
Therefore, the answer is option D: halfway down the cliff.
ty so much :D
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The potential energy of an object is determined by its position or height above a reference point, while the kinetic energy depends on its motion or speed.
In this scenario, the potential energy of the banana is highest at the top of the cliff when it is not yet in motion, and gradually decreases as it falls. On the other hand, the kinetic energy starts at zero and increases as the banana gains speed during its descent.
The potential energy and kinetic energy of the banana are equal when the potential energy has been completely converted into kinetic energy. This occurs at the bottom of the cliff when the banana is about to hit the ground.
Therefore, the correct answer is A) at the bottom.
To determine the location where the potential energy and kinetic energy of the banana are equal, we need to examine the process of energy conversion.
Initially, when the banana is at the top of the cliff, it possesses only potential energy. As it falls freely due to gravity, this potential energy gets converted into kinetic energy. According to the law of conservation of energy, the total mechanical energy (sum of potential energy and kinetic energy) of the banana remains constant throughout.
At any given point during the fall, the total mechanical energy is divided in different proportions between potential and kinetic energy. The key here is to determine the precise location where the two energies are equal.
Let's analyze the options:
A) At the bottom:
At the bottom of the cliff, the banana has lost all its potential energy since it has reached the lowest point. Therefore, the potential energy is zero and all the mechanical energy has been converted to kinetic energy. Hence, the potential energy and kinetic energy are not equal at the bottom.
B) At the top:
Initially, at the top of the cliff, the banana has maximum potential energy and zero kinetic energy. As it falls, the potential energy decreases, and the kinetic energy increases. Therefore, the potential energy and kinetic energy are not equal at the top.
C) A quarter of the way down:
At this point, the potential energy has decreased, but it is still significant compared to the kinetic energy. The banana has not fallen far enough for the kinetic energy to surpass the potential energy. Thus, the potential energy and kinetic energy are not equal a quarter of the way down.
D) Halfway down:
At this location, the banana has fallen for half the distance, resulting in a significant reduction in potential energy. Simultaneously, the kinetic energy has increased substantially. Therefore, at this point, the potential energy and kinetic energy are equal. Therefore, the answer is D) halfway down.
So, the potential energy and kinetic energy of the banana are equal halfway down the cliff.