Question

You have an internship working for the National Park Service. They start you off in the laboratory which tests possible new equipment. Your first job is to test a small cannon used to prevent avalanches in populated areas by shooting down the velocity of the projectile as it leaves the cannon (muzzle speed) so that the range and trajectory of the cannon can be determined. heavy snow concentrations. You want to find out Lab, Initial Lab, Final The cannon you are testing weighs 260 kg and shoots a 15 kg projectile. During the lab tests the cannon is held horizontal in a rigid support so that it cannot move. Under those conditions, you use video analysis of the projectile to determine that the muzzle speed is 300 m/s. Field, Initial Field, Final When fired in the field, the cannon is not rigidly attached to the ground, but it is free to move (recoil) when it is fired. There are ropes attached to anchors so that the cannon can only recoil 0.5 m. You must predict the projectile's muzzle speed under field conditions, when it recoils. The cannon is fired horizontally using cannon shells which are identical (same mass, same amount of gunpowder, etc.) to those in the laboratory In both the laboratory and the field test, we'll consider the system of the cannon, the cannonball. and the gunpowder. (A) In both cases, we'll assume the energy is conserved, meaning the (same amount of) energy from burning the gunpowder becomes kinetic energy of the cannonball (in the lab) or the can- nonball and the cannon (in the field). In other words, the total kinetic energy after the explosion is the same in both cases. Now, describe the two firings, in the lab and in the field, in terms of momentum. (B) Set up the problem with knowns, unknowns, and equations that can be solved to get the projectile's muzzle speed in the field. C) Calculate the projectile's speed in the field, first with variables and then solve for the value. (D) If you want the projectile velocity in the field Unield to be 98% of the velocity in the lab Unlab, or Up.field 0.98 Ub.lab, what will the mass of your cannon me need to be?

Answer 1

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