How Many 100W Bulbs Can Be Powered by Converting Water's Potential Energy?

[ROCKSTAR99]

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.

 

[DrClaude]

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.

 

[ROCKSTAR99]

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 ?

 

[drvrm]

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]

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.

 

[ROCKSTAR99]

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

 

[ROCKSTAR99]

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 ?

 

[drvrm]

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]

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.

 

[ROCKSTAR99]

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.

 

[DrClaude]

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.

 

[ROCKSTAR99]

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]

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.