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# calculating energy

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hey all, by no means am i a physics major, or professional, but i know a little bit...with that in mind, i was posed a question by a fellow fireworks enthusiast over the weekend.

so here goes. basically we're trying to calculate the recoil force of an aerial shell upon launch. there's a second part of the question that might be a little too complex given the information we have, but i'll get to that in a bit.

ok, so lets say the shell weighs 100g, and attains a height of 200ft. given that information, what is needed to calculate the force of the shell in motion, as well as the mortar tube it's shot from (given that every action has an equal and opposite reaction).

the second part is, upon liftoff, several of these mortar tubes are driven into the ground, lets say a few inches, call it 3. without knowing the density of the ground, is there any way of knowing how much force the ground is actually absorbing, and in effect, robbing from the shell?

thanks in advance.

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hey all, by no means am i a physics major, or professional, but i know a little bit...with that in mind, i was posed a question by a fellow fireworks enthusiast over the weekend.

so here goes. basically we're trying to calculate the recoil force of an aerial shell upon launch. there's a second part of the question that might be a little too complex given the information we have, but i'll get to that in a bit.

ok, so lets say the shell weighs 100g, and attains a height of 200ft. given that information, what is needed to calculate the force of the shell in motion, as well as the mortar tube it's shot from (given that every action has an equal and opposite reaction).

the second part is, upon liftoff, several of these mortar tubes are driven into the ground, lets say a few inches, call it 3. without knowing the density of the ground, is there any way of knowing how much force the ground is actually absorbing, and in effect, robbing from the shell?

thanks in advance.

You need to learn a bit more physics. You are using the notion of "force" in situations in which it does not apply.

When one launches a projectile recoil is the result of conservation of momentum. Recoil momentum is quite easy to determine, being equal to the combined momentum of the projectile and the propelling as.

Recoil force, on the other hand is very difficult to determine. The time integral of the recoil force is equal to the recoil momentum. But the actual time history of that force is determined by the boundary conditions -- the elasticity of the absorbing media, including any non-linearities such as viscoelasticity.

Very little is "robbed from the shell" in any recoil scenario. A tiny amount of recoil motion while the projectile is in the barrel may result in a minuscule pressure drop and/or reverse force on the projectile, but that effect is of little importance.

There is no such thing as "the force of the shell in motion". There is of course kinetic energy and momentum. If you know the height attained and the initial launch angle you can determine the muzzle velocity -- easily if air resistance is neglected, and with numerical aid if not (given knowledge of atmospheric properties and shape of the projectile.) If you are launching vertically mgh=1/2 mv^2 so v = sqrt(2gh).

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basically, im trying to determine the force applied to the ground over the area of the bottom of the mortar tube. im not sure if it would be easier to figure for N, or Ns.

so lets say an 8" shell weighs in at 7lbs even, and at apogee, gets 800ft above the ground and takes 5 seconds to attain that height. given the information, how would i calculate the net force applied to the mortar?

like i say, im pretty "in the dark" so-to-speak, in regards to physics.

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so lets say an 8" shell weighs in at 7lbs even, and at apogee, gets 800ft above the ground and takes 5 seconds to attain that height. given the information, how would i calculate the net force applied to the mortar?

From that information you can't determine the peak force, or even the average force. In fact, since you don't know the propellant characteristics, or even mass, you can't calculate the recoil momentum.

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