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Explosions

Momentum ideas are also useful in explaining explosions. If we blow up a balloon and then burst it, the pieces of rubber fly off in all directions. The momentum of the balloon was zero before the explosion and therefore the total momentum of all the pieces of rubber after the explosion must also be zero. It is important to remember here that momentum is a vector and so the direction of motion of the pieces is important.


This principle can be studied with two spring-loaded trolleys. If they are put back to back and the spring in one is released they will explode. Both trolleys move apart with the same speed because they are of equal mass. In the second diagram trolley 2 moves off with half the speed of trolley 1 as it has twice the mass.

The recoil of a gun can be explained in the same way.

Before the gun is fired, the momentum is zero and so after firing the momentum must still be zero, the momentum of the shell is equal and opposite to that of the gun. A simple way of looking at it is this. If the shell is 100 times lighter than the gun then the shell will move off 100 times faster than the gun recoils. Remember that in explosions the lighter portion moves off faster than the heavier one.

Example problems
(a) A gun of mass 100 kg fires a shell of mass 1 kg. The charge explodes and forces the shell up the barrel at high speed. If the shell leaves the barrel at 200 m/s what is the recoil velocity of the gun?

Momentum before explosion = 0 therefore momentum after explosion = 0
If the velocity of the shell is v m/s: Momentum after explosion = 1x200 + 100v
Therefore v = - 200/100 = 2 m/s.

(b) a girl jumps onto a 75 kg shopping trolley that was moving at 1.5 m/s. The girl has a mass of 50 kg and was standing still when she jumped on.
What is the final velocity of the girl and trolley?

Momentum before collision = Momentum after collision
75x1.5 = 125v      v = 0.9 m/s

schoolphysics: Recoil of a cannon animation

To see an animation of the reecoil of a cannon when it fires a shell click on the animation link.


 

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