Explosions are a fun way to learn how to apply the law of momentum to an object that starts as a single object, and after the explosion, scatters into fragments that each have their own momentum, like a firecracker. The vector sum of all the parts of the system could be added together to find the total momentum after the explosion, which equals the total momentum before the explosion. If we put a cannon on wheels, we can find the momentum change of the cannon ball and the acceleration of the cannon after it fires:
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This is an example of the distributive property. We start with 0=MV+m(v+V) then, we multiply m times v and m times V. This becomes 0=MV+mv+mV. Then we collect the terms so the equation is 0 = V (M + m) + mv.
At 4:35 where did the extra little ‘m’ come from?