Ideal Simple Machines: Input Work & Power Equal Outputs

[fisico30]

Dear Forum,

in the case of ideal simple machines the input work is exactly ideal to the output work.
The efficiency is 100%.


In some cases the input power is equal to the output power, but not always: when we push a box up an inclined plane we need a smaller force for a longer distance. It will take a longer time (less output power hence) to push the block to the final height than if we simply lifted the block.

In the bicycle case instead, we have both input work=output work and input power= output power. Thanks to the chain, the work is transferred from the front wheel to the rear wheel in the same interval of time. There is some coupling.

How can we phrase the general requirement to achieve input power = output power in simple machines?

Any comment or correction?
thanks
fisico30

 

[berkeman]

Dear Forum,

in the case of ideal simple machines the input work is exactly ideal to the output work.
The efficiency is 100%.


In some cases the input power is equal to the output power, but not always: when we push a box up an inclined plane we need a smaller force for a longer distance. It will take a longer time (less output power hence) to push the block to the final height than if we simply lifted the block.

In the bicycle case instead, we have both input work=output work and input power= output power. Thanks to the chain, the work is transferred from the front wheel to the rear wheel in the same interval of time. There is some coupling.

How can we phrase the general requirement to achieve input power = output power in simple machines?

Any comment or correction?
thanks
fisico30

What is the equation relating work and power? Writing that equation out should help you to answer your question, I think.

 

[fisico30]

Sure,

Power=work/time

so work= power*time

input work=output work

I guess your point, Berkeman, is that if work remains the same, then the product power*time is the same but power and time can be different for the input and output situations: clearly the larger the power the smaller the time.

In the inclined plane case the time is large and power is small.
In the bicycle case, the work (energy) transferred from the front wheel to the rear wheel is the same and also the power is the same since the time is the same...

thanks,
fisico30