Why are low impedance speakers harder to drive than high impedance speakers

I don't understand the electrical reason for this. I look at it from a mechanical point of view. If I have a spring that is of less resistance, and push it with my hand, it takes little effort, and I am not working hard to push it. When I have a stiffer spring (higher resistance)  I have to work harder to push it. This is inversely proportional when we are looking at amplifier/speaker values.

So, when I look at a speaker with an 8 ohm rating, it is easier to drive than a speaker with a 4 ohm load. This does not make sense to me, although I know it to be true. I have yet been able to have it explained to me that makes it clear.  Can someone explain this to me in a manner that does not require an EE degree?


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Since the OP thinks in mechanical terms, this analogy may best describe how speaker loads affect an amp.
Imagine the amp is a somewhat fragile flywheel that will fly apart at a certain RPM. If you apply a resistance (an 8 ohm speaker load in electrical terms) to the flywheel that is sufficient to prevent the flywheel from reaching critical speed it will not break. If you remove part of the resistance (think 4 ohm speaker) the flywheel will speed up. If you remove enough of the load, you eventually reach a point where the flywheel is spinning so fast it fails. Replace the concept of the flywheel speed with power output from the amp. The power an amp will produce is inversely proportional to the resistance to current flow. More resistance keeps the amp in check so to speak.
Hi all, 
This is my first post in this forum :)

According to Al's information, having the two extreme examples, 
I have the exact opposite question: 
For headphones, why do we need good, high, powered amp to 
move headphones with very high impedance (300-600 ohms). 
According to the ohm equasion, for the same power, as long as the amplifier "understand" that the output is not disconnected (as the "100,000 ohms" al's example), than the amp needs only a tiny current to "drive" the headphones.
What am I missing here? 

Thank you all!