# Watt (Power) better conceptually explained.

Here is the usual definition of Watt given by wikipedia:

One Watt is rate at which work is done when an object's velocity is held constant at one meter per second against constant opposing force of one newton. (or 1 N x m/s)

Now I do NOT get this conceptually. So I like to imagine the scenario in space (which i always use as the frame of reference for my thought understandings).

I have a space ship that ALWAYS generate one Watt. It starts at speed 0 m/s relative to me.

Shouldn't this space ship accelerate forever (or up to the speed of light?). As far as I know, a spaceship going at 1 m/s is the same as one going to 0 m/s in terms of energy needed. I don't understand the above definition of Watt.

Can someone describe to me what will this spaceship do if it ALWAYS and ONLY puts out one watt???

Thank you

## Answers and Replies

They key part of the definition was the "against constant opposing force of one newton". A watt is just a measure of power which is joules per second, in your spaceship example there is no opposing force so it will indeed accelerate since there is net work done by the spaceship.

Thanks JHamm,

So can i ask you. If the spaceship has a mass of 1 gram and constantly puts out 1 Watt of power, what would be the acceleration?

Thanks!

Also, how many watts would it be if one gram object's velocity is held constant at TWO meter per second against constant opposing force of one newton.

Is it 2 Watt? If so why?

From what I understand an object traveling 2 m/s versus and object traveling 1 m/s pushing against a constant 1 newton force should be the same. I always thought in space speed doesn't matter, but rather, the change in speed matters (as acceleration, not speed, is due to force).

Doesn't an object in motion shall remain in motion?

nasu
Gold Member
You should better start with the basic definition: the power is the rate of doing work or transferring energy.
The Wiki definition is just a special case.
If you have uniform motion as described in the Wiki definition, then the force you are looking at is constant. If the displacement is along the direction of the force, the work done is W=f*d and the power will be P=f*d/t or P=f*v
The power depends on velocity. Higher velocity means larger distance traveled in 1 s, more work done in the same 1s and this means more power.

For the case of an accelerating object (a single, non balanced force for example), if the force is constant the power will increase as the velocity increases.
If the power is constant, the force decreases as the speed increases (think about the gear shifting in a car or bicycle).

• Stephanus
Hi Nasu

Im not sure i understand. But thanks for trying

Doc Al
Mentor
Instead of your spaceship example, think of pushing a box along a floor against friction. If the friction is 1 N and you are pushing the box at a steady 1 m/s, then you are delivering 1 Watt of power to the box.

Would you not agree that to push the box 100 m at constant speed would require 1N x 100m = 100 Joules of work?

And if you were to cover that distance in 100 seconds you'd require 1 W of power, but to do the job in 1 second you'd need 100 W.

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Doc Al
Mentor
Also, how many watts would it be if one gram object's velocity is held constant at TWO meter per second against constant opposing force of one newton.

Is it 2 Watt? If so why?
Yes. Because every second the pushing force of 1 N must act over 2 m. That's 2 J of work per second.

From what I understand an object traveling 2 m/s versus and object traveling 1 m/s pushing against a constant 1 newton force should be the same.
What would be the same? Sure the net force is zero in both cases, but we're talking about how much power must be applied by the pushing force.
I always thought in space speed doesn't matter, but rather, the change in speed matters (as acceleration, not speed, is due to force).
What matters is that something is pushing against resistance.

Doesn't an object in motion shall remain in motion?
As long as the net force is zero.