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No. The size-weight of the bullet also affects the knockdown power.

Power, kinetic energy, force and momentum: they are all related, and each one carries a 'mass' component.

It is, more expressly. the size of the Force or momentum of a moving object that determines its affect on other objects; and force and momentum are directly determined by both - the speed of the moving object and the size of its mass.

As it requires a greater force to move the larger bullet in the first place, which therefore means greater energy expended to do so, so at the other end that greater energy is conserved in the larger bullet, and therefore hits its target with greater force and energy.

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