# Potential energy to watts

OP warned about not using the template
Could anyone help me with this sum - To generate electricity, 180000 kg water is dropped from a height of 50 m (let g = 10 m/s^2). If half the gravitational potential energy is converted to electric energy, how many 100 W bulbs can be lit ?

Formula - Ep = mgh

I calculated the potential energy to be 90000000 J. Half of it is electric energy = 45000000 J. I am at a loss from here.

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DrClaude
Mentor
I calculated the potential energy to be 90000000 Js. Half of it is electric energy = 45000000 Js.
The units don't work. Energy should be in joules. You will also need a time so you can convert the power consumption of the light bulbs into a total energy consumption.

The units don't work. Energy should be in joules. You will also need a time so you can convert the power consumption of the light bulbs into a total energy consumption.
So, is the question wrong ?

I calculated the potential energy to be 90000000 Js. Half of it is electric energy = 45000000 Js. I am at a loss from here.
why not use the conversion table of watt and joule? one joule per second is equal to one watt!
when water is coming down -it should have some rate of flow - so you should not write Js only -whether s is for time or its joules?

DrClaude
Mentor
So, is the question wrong ?
Not necessarily. It is not very well formulated, but there are different ways of coming up with a reasonable answer.

why not use the conversion table of watt and joule? one joule per second is equal to one watt!
when water is coming down -it should have some rate of flow - so you should not write Js only -whether s is for time or its joules?
s is for seconds

Not necessarily. It is not very well formulated, but there are different ways of coming up with a reasonable answer.
Lets say 180000 kg of water fall per hour. Now, can we find an answer ?

s is for seconds
does it mean joule in a second then it is J s^-1 or J/s -it means the rate of flow is there -then you can convert directly to watt and calcilate number of light bulbs.

DrClaude
Mentor
Lets say 180000 kg of water fall per hour. Now, can we find an answer ?
Yes. You first need to figure out how much gravitational potential energy there is in that mass of water.

does it mean joule in a second then it is J s^-1 or J/s -it means the rate of flow is there -then you can convert directly to watt and calcilate number of light bulbs.
Using the mgh formula, I multiplied 180000 kg, 50 m and 10 m/s^2. It gave 90000000 kgm^2/s^2. I made a mistake, kgm^2/s^2 equals just Joules and there is no seconds.

• drvrm
DrClaude
Mentor
Using the mgh formula, I multiplied 180000 kg, 50 m and 10 m/s^2. It gave 90000000 kgm^2/s^2. I made a mistake, kgm^2/s^2 equals just Joules and there is no seconds.
Correct. Now you need to convert it to power, using the assumption you have made about the rate of flow.

Correct. Now you need to convert it to power, using the assumption you have made about the rate of flow.
Ok, so 90000000 J is converted to 45000000 J of electric energy. As 1 watt = 1 joule per second, 45000000 J/ 3600 s gives 12500 W. So, is the answer 125 bulbs (12500 W/ 100 W) ? If it is, Thanks a lot.

DrClaude
Mentor
Ok, so 90000000 J is converted to 45000000 J of electric energy. As 1 watt = 1 joule per second, 45000000 J/ 3600 s gives 12500 W. So, is the answer 125 bulbs (12500 W/ 100 W) ? If it is, Thanks a lot.
That sounds fine.

• ROCKSTAR99