Relationship between volts and Mechanical Energy

Question

I am studying Electrical Engineering and I came across one definition of the volt being defined as follows:

V = J / C

Where "V" is voltage measured in "volts", "J" is energy measured in "joules" and "C" is charge measured in "coulombs". If this definition is correct, it would appear that a 10 V battery should be able to produce 10 joules of energy per coulomb of charge. My question is, what is the relationship between volts and Mechanical Energy?

The reason I bring this up, is because if we assume that the acceleration due to gravity is 10 m/s², the amount of energy required to move 1 kg of water a distance of 1 meter vertically is equivalent to 10 joules. I used the following formula:

F = m * a = (1 kg) * (10 m/s²) = 10 newtons.

W = F * d = (10 N) * (1 m) = 10 joules.

Does this mean that using a 10 V battery, I should be able to create a device that is able to move 1 kg of water a distance of 1 meter up in the air? I am trying to better understand the relationship of volts as a difference in Electrical Potential between two points in space and somehow using this potential to move objects with a certain mass a certain distance. Perhaps I am mixing different physics concepts together. Any insight into this would be appreciated. Cheers.

Answer 1

Well yes, energy is energy. The only problem is converting it from one form of energy to another form of energy.

And you cannot take a random battery with 10 V. It has to have enough charge to be able to do the work.

So in a perfect world, you would build some magic mechanism, which would be able to lift something at 100 % efficiency when you supply it with 10 V. You want to lift 1 kg up 1 m, so you need approximately 10 J.

How much charge would you need? Well 1 C, but that's not a really useful measure you usually get with a battery. Most of the time you get something like amperehours or watthours. 1 Ah is equal to 3600 C (1 A is 1 C per second). So your battery would just need to have 1/3600 Ah. Or 2.8 mWh. This is so little energy - your phone could do this work surely 20000 times before running out of juice.

But your phone is running on 3.6 V - the voltage doesn't really matter (it will in a practical application), if you restate the equation, you will get J = V * C, so if you have less voltage you just need more charge to get the same energy.

Problem is, in reality you will have losses everywhere and you might get something like 80 % efficiency (conversion losses, friction in the mechanic) or something and so you will need more energy to do the work.

Devices like this do exist - they are called elevators.

Answer 2

a 10 V battery should be able to produce 10 joules of energy per coulomb of charge.

Yes. As you say, that's straight from the definition of a volt.

what is the relationship between volts and Mechanical Energy?

You already answered that yourself. The voltage is a measure of how much energy each Coulomb of charge has.

This has nothing to do with "Mechanical" energy. A joule is a joule whether that's a coulomb at 1 volt potential, A newton of weight raised 1 meter, or something else.

Answer 3

Does this mean that using a 10 V battery, I should be able to create a device that is able to move 1 kg of water a distance of 1 meter up in the air?

If that battery can supply 1 Amp for 1 second ... yes. 1 Amp is 1 coulomb/second, and you dropped the coulomb from your actual question though it was, correctly, present in your introduction.

Connect it to a 100% efficient electric motor, winding string onto a drum, to raise the weight. 10V will translate to the motor running at a specific speed, and the torque required to raise the weight will draw a specific current (maybe 1 Amp) from the motor. If it draws less current ( 0.5A) that translates to less power (5W) , so your 10J work will take longer ( 2 seconds).

The trick, of course, is to find a 100% efficient motor, A small one like that (10W) is likely to be 50% at best, up to 90% above the horsepower range.