Confusion with work and constant velocity

[okgo]

Homework Statement

So I'm confused about work and constant velocity. In a sailboat example, if the boat is going at constant velocity then there is no acceleration, therefore no net Force and no work.

However, let's say there is an elevator being pulled upward by a pulley at constant velocity. This would mean the elevator is not accelerating so no net Force, and then no work.
But I'm confused about PE. Since the elevator is being pulled upward, wouldn't PE increase and isn't change in PE = W? So work would increase with increase in PE?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

So I'm confused about work and constant velocity. In a sailboat example, if the boat is going at constant velocity then there is no acceleration, therefore no net Force and no work.

However, let's say there is an elevator being pulled upward by a pulley at constant velocity. This would mean the elevator is not accelerating so no net Force, and then no work.
But I'm confused about PE. Since the elevator is being pulled upward, wouldn't PE increase and isn't change in PE = W? So work would increase with increase in PE?

Not exactly. For the ship there is work against friction in pushing the boat through the water, likely even can be somewhat determined from the weight of the water that is churned by the propeller. There is no acceleration, so no work goes into kinetic energy of the mass of the ship.

For your elevator there is no work again going into kinetic energy, because there is no change in speed. But there is a change in potential energy. For instance if you cut the rope and the elevator fell back to the starting point there would be that much kinetic energy carried by the elevator as it passed that point going down.

 

[nlightner]

In the sailboat example, you are correct in saying that if the boat is moving at a constant velocity, there is no acceleration and therefore no net force and no work. This is because work is defined as the product of force and displacement, and since the boat is not changing its velocity, there is no displacement and thus no work.

In the case of the elevator being pulled upward at a constant velocity, the situation is a bit different. While it is true that there is no net force and no work being done on the elevator, there is still a change in potential energy (PE). This is because the elevator is being lifted to a higher position, which means its distance from the ground is increasing and thus its PE is also increasing.

To understand this better, you can think of it in terms of the work-energy theorem, which states that the net work done on an object is equal to the change in its kinetic energy. In the case of the elevator, there is no change in its kinetic energy (since it is moving at a constant velocity), but there is a change in its potential energy. This change in potential energy is equal to the work done on the elevator, which in this case is being done by the pulley system.

So in summary, while there may not be any net force or work being done on the elevator, there is still a change in its potential energy, which is equal to the work done on it. This is why the change in PE is equal to W in this scenario. I hope this helps clarify your confusion.