Is it better to jump with a long foot or short foot?

The cases below only differ by whether the in-lever or out-lever is bigger. Which will jump higher?

Ignore contraction dynamics & imagine the body is constrained to go straight up.

Answer and discuss below 馃憞


Which will jump higher?

The results are in! Although a majority said (a), for this particular setup, (b) jumps higher.

This is NOT a general rule in biological jumpers, and is particular to how we've set up the problem (notably, no force-velocity relationship)

All that matters is the amount of work done by the muscle. Since there is no force-velocity relationship, the work done is proportional to the shortening distance. Case (b) wins because the larger in-lever allows the muscle to shorten more

We have an intuition that (a) should be better because biological jumpers look like that. But this is to accommodate power-velocity relationships in muscle, which this setup doesn't have.

My intuition was initially drawn to (c), but the physics clearly show (b) as the winner here. A good reminder to check model assumptions!

If anyone has a good real-world example analogous to this setup, let me know! Force-velocity is pervasive, though

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