Which stream has the greatest potential energy on the top: stream with steeper slope or stream with gentle slope?

i think the stream with the steep slope but i'm not entirely sure.

Answered by chipman98 | 2024-06-10

The stream with the steeper slope has the greatest potential energy at the top.
Potential energy (PE) is given by the formula PE = m g h , where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point. For a stream, the relevant height is the vertical distance from the top of the stream to the reference point, which is typically the base of the stream or the point where the potential energy is fully converted to kinetic energy.
A steeper slope means that for a given horizontal distance, there is a greater change in vertical height ( h ) compared to a gentle slope. Since potential energy is directly proportional to height, the stream with the steeper slope will have a greater h and therefore a greater potential energy at the top, assuming the mass of water ( m ) is constant and the acceleration due to gravity ( g ) is a constant value of approximately 9.81 \, m/s^2 \
To illustrate this with a simple example, consider two streams, A and B, both starting at the same height and flowing for the same horizontal distance. Stream A has a steeper slope, and Stream B has a gentle slope. If we denote the horizontal distance as d and the angle of the slope with respect to the horizontal as θ , the height h can be calculated using trigonometry as h = d ⋅ sin ( θ ) . Since sin ( θ ) is greater for a steeper slope (larger θ ), Stream A will have a greater h and thus greater potential energy.
Therefore, the stream with the steeper slope will have the greatest potential energy at the top, all else being equal."

Answered by AnkitM | 2024-06-24

The stream with the steeper slope has the greatest potential energy at the top because it has a larger vertical height compared to a stream with a gentle slope. The potential energy formula PE = m g h shows that greater height leads to greater potential energy. Therefore, steeper slopes result in more potential energy due to higher elevations.
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Answered by AnkitM | 2024-12-23