Cannon recoil WITHOUT projectile?

[bunchie]

Hi,

I am trying to figure out why I think that if a cannon fires a heavy projectile, the cannon's recoil is greater than for a cannon that doesn't fire any projectile at all.

Is this correct? Will the cannon firing a heavy projectile have a greater recoil than the empty, firing cannon? It seems that the pressure from the gases would be the same for both cannons, so both will be pushed back the same way.

Also, when a rocket takes off, don't the exploding gases somehow "push back" against the launching pad to accelerate the rocket? Why do I think that the rocket taking off is like a person on rolling skates pushing against a wall to start moving? Say the person was holding a powerful fan. Wouldn't they go faster if they initially directed the fan's jet against a wall rather than just air?

Please help me clarify my thought process. I've searched through other threads and haven't been able to find answers.

Thanks.

 

[Integral]

Look into conservation of momentum for the reasons behind your correct assumption about the cannons recoil.

As for the rocket. How could the rocket know what happens to the escaping gases when they are away from the rocket? Why do the escaping gases continue to propel the rocket when it is far from the pad?

 

[K^2]

Pressure in the cannon firing a heavy projectile is significantly higher, because the projectile restricts expansion of the gas.

Conservation of momentum is the easy way to see that the recoil must be greater, but yes, the recoil is ultimately caused by gas pressure, so you can look at it from either perspective.