a 250-kg rock falls off a cliff and comes to rest on the ground, which is 40 m below the cliff . At what point is the rock's potential energy at maximum?
The rock's potential energy is at its maximum when it is at the top of the cliff. This is because potential energy is directly proportional to the height above the reference level. In this case, the reference level is the ground, and as the height increases, the potential energy also increases.
Therefore, the point at which the rock's potential energy is at its maximum is when it is at the top of the cliff before it falls.
To determine the point at which the rock's potential energy is at its maximum, we need to consider the relationship between potential energy and height.
The potential energy of an object in a gravitational field is given by the formula:
Potential energy = mass × gravitational acceleration × height
In this case, the mass of the rock is 250 kg, the height is 40 m, and the gravitational acceleration is approximately 9.8 m/s^2.
Now, let's analyze the situation step by step:
1. Initially, when the rock is still at the top of the cliff, its potential energy is at its maximum. At this point, the entire height of the cliff is contributing to the potential energy, and there is no loss due to height yet.
2. As the rock falls, its height decreases, and consequently, the potential energy decreases. The potential energy is converted into kinetic energy, which increases as the rock accelerates downward.
3. Before reaching the ground, when the rock's height becomes zero, its potential energy becomes zero as well, and all the potential energy is converted into kinetic energy.
Therefore, the maximum potential energy of the rock occurs at the top of the cliff, just before it falls.