YOu fire two bullets through a chronograph. The chronograph gives you speeds of

Question

YOu fire two bullets through a chronograph. The chronograph gives you speeds of the bullets. YOu loaded the cartridges, so you know the mass of the bullets. One bullet is slow and heavy. The other bullet is fast and light. You calculate that the two bullets have the same momentum when exiting the muzzle of your gun.

Which cartridge had more powder? The powder charge contains the chemical energy that is converted to large volumes of hot gas that pushes the bullet through the barrel. The barrel of the gun is a cylinder (ignore rifling).

Explanation / Answer

The hot gas will be putting a force on the bullets
F = dp/dt
each of the bullets experienced the same dp (change in momentum)
I assume that because the barrel length is held constant, t will be different for each of the bullets

The lighter bullet will have to be going faster to reach the same momentum as the larger bullet. Thus, it must have spent less time in the barell of the gun, correct? (v = r/t)

Thus, t must have been smaller for the lighter bullet.

Then if F = dp/dt, the force put on the smaller bullet must have been larger.

Using this logic, I assume that the smaller bullet cartridge must have had more powder.

Thoughts?

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