If you are bicycling fast enough you can cross a wooden plank spanning ditch
before the plank breaks.

Normally we say this is because it takes time for the plank to deform and
break when subjected to a weight.

However, consider for a moment an alternative and naive(?) explanation: it
because you weigh less when you are moving than when you are stationary. The
idea is your motion reduces your gravitational mass ( independently of your
inertial mass) while gravitational acceleration remains unchanged.
 
While this theory is probably wrong, it would be easy to test in practice.
See my 40k pdf file for an illustration of the theory.

http://web.ncf.ca/eo200/dynamics/testing_weight.pdf

Another test would be to take a bathroom scale on a plane or a train and
weigh oneself. Has anyone done this by chance?

Harry

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