The problem is: if 2 blocks, one fouble mass, are moved the same distance d, pushed by the same force, work kinetic theorem ("" 9nly empirical proved) says they ll achieve same final kinetic energy. But does kinematics prove it? I. E Kinetic energy is prop to mass and velocity sq. Ligher block will have deficiency in mass proportionality (1/2) while heavier mass has deficiency in final speed, according to Newtons. Is this deficiency prop to 1/2 so it cancels out and agreement with theorem is met?
Answer
V=sqr 2ad or so for heavier block, acceleration is half according to Newtons.
This means velocity of heavy is prop to sqr (1/2) compare to prop of sq1 for light. Inside sq root, half cancels with 2 so we have sq ad vs sqr 2ad. We need to examine if these are double of each other, or if we divide their squares ad/2ad gives 1/2 or velocity of heavy is half.
To do this, we ponder that heavy has double prop with mass, light double with velocity, they cancel and this agrees with kinetic work theorem.
Sorry no mistake. Where is the non theorem based truth i intended to ask
This is also the reason why kinetic energy is defined as prop to m v sqr: this def is compatible with (and invites) a universal energy def (aka work, since kinetic and potential are just special non generic energy types) that does the promise of the idea i.e a constant of motion at a differing (absolute) time progression common spatial point in space if force is applied in 2 unequal masses at same initial spatial coordinate, a basic completeness /closure demand for mechanics. Its not the other way around as its often present Ed. This proof pathways, on this though experiment, is a basic part of classical non relativistic mechanics
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