# Why don't we take kinetic energy into account when finding the change in potential energy?

An engine draws water from depth of $$10 \;\text{m}$$ with constant speed $$2 \;\text{m/s}$$ at rate of $$1 \;\text{kg/s}$$. What is the power of the engine?

While solving the question, I found that we involved both kinetic energy and potential energy. However, in general, when we are solving questions like

Find the change in energy when an object moves upwards by a given height

why do we only talk about potential energy or use the simple formula($$\mathbf{F} \cdot \mathbf{s}$$) and not involve kinetic energy in that? Because during the movement, the speed must be non-zero, otherwise it's impossible to move an object.

• Hi, please don't ask an entire question in the title. The title is supposed to be a summary of your question. I have edited this question to make clear the conceptual question inside. Commented Jul 6, 2021 at 12:41

## 2 Answers

If the velocity is constant the kinetic energy will not change. Also if we are not given the details such as velocity after work, how can we talk about the change in kinetic energy? In your problem it is given that (or you have to assume that) the object is moving with a constant velocity (I am here referring to your second problem), thus you have nothing to worry about change in the kinetic energy. However, when talking about the engine, it gives a velocity to the water as well as potential energy. As water had zero velocity before, the kinetic energy increases surely.

• Is that because at the the height the object have come, it will have total of energy as potential energy and so we need to worry about? So, if they had ask energy in between the interval, then we might had to worry about that? But even in that case, we only find potential energy at the interval and subtract with the final. Why is that then? And in the 1st question, why can't we just do it like mgh at 10 meters and need not to worry about ke coz it would zero at max height? Commented Jul 6, 2021 at 12:33
• But even when the object moved. It had zero velocity in the starting and we displaced it. Commented Jul 6, 2021 at 13:18
• Yes, in that case KE is changed. I think you have probably misunderstood the two situations given above by yourself. Carefully read the answer and think again.
– ACB
Commented Jul 6, 2021 at 14:13

Good question. The problem is an incompletely described situation. Such questions are common, and it's up to the reader to make reasonable assumptions about the missing information.

In the case you present we are told the speed and that it's constant. There are several possibilities consistent with that wording. One is that it never starts and never stops. Another is that we are interested only in the inteval immediately after it starts and immediately before it stops. This is the usual assumption in projectile motion problems. Those questions typically ask "what is the final velocity". Well, if it hits the ground and stops the final velocity is zero. That's not what's meant. Another possibility is that we do include stopping and starting. In that case the gain in KE at the begining is lost at the end. In all of those cases the change in KE is zero.

Here are two more possibilities: 1.) it starts at zero speed but passes through the end location at 2 m/s and 2.) motion begins at 2 m/s before we start paying attention, but stops at the top. In these two cases the KE does change, and we do need to consider it. I suggest that these two possibilites are less reasonable than the three above. These two lack the symmetry that the first three have.

The reasonable assumption is KE is constant.