# Why does Potential Energy (PE) = Useful Energy Output?

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#1
A crane lifts a 100kg block through a height of 8m. The motor uses 150kJ of energy during this lift.

Calculate the efficiency of the motor.

The efficiency formula is used and potential energy (PE) is used for "useful energy output":

• efficiency = useful energy output / total energy input

However, I don't understand why PE is used for the useful energy output. PE is the total amount of stored energy. This isn't the total amount of "useful energy" as the this stored energy can be released in multiple forms, some of which useful some of which, not useful. Therefore if we are to use PE within this efficiency formula then it should read.

• efficiency = total stored energy / total energy input

Really need a decent explanation with this as the definitions for PE and useful energy seem to me, to be really muddled up by my text book. I'm sure I have it wrong as i'm battling what is essentially, well known physics but still, i'm really confused.

Thanks
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5 years ago
#2
(Original post by Tom.Dunwoody)
However, I don't understand why PE is used for the useful energy output. PE is the total amount of stored energy. This isn't the total amount of "useful energy" as the this stored energy can be released in multiple forms, some of which useful some of which, not useful. Therefore if we are to use PE within this efficiency formula then it should read.

1st law of energy conservation: Energy can neither be created nor destroyed but can convert from one form to another.

K.E. was used to lift the block 8m. i.e. the kinetic energy of motion was converted to potential energy as a result of the 100kg mass attaining that height. If the block is released, it will fall to the ground under the force of gravity. P.E. will convert to K.E. as it does so.

However, machines are not 100% efficient. Some of the energy used by the machine will be wasted overcoming friction/motor losses etc. which are converted to heat whilst the rest is stored as PE as the block is raised.

Hence the efficiency of the machine will be the ratio between the final stored PE (useful energy output by the machine) and the total energy consumed by the machine (energy input).

The difference between the energy input and the stored energy must therefore be the energy lost through friction.
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#3
I see so, what the machine can actually produce to lift the weight divided by the total energy consumed by the machine.

Therefore total energy cosumed by the machine = P.E + waste energy (friction, heat, sound ect) ... I hope i'm right =]
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5 years ago
#4
(Original post by Tom.Dunwoody)
I see so, what the machine can actually produce to lift the weight divided by the total energy consumed by the machine.

Therefore total energy cosumed by the machine = P.E + waste energy (friction, heat, sound ect) ... I hope i'm right =]
Correct. 0
#5
Brilliant, thanks so much for your help =]
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