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601-F: Conservation of Momentum 4: Explosions

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601-F: Conservation of Momentum 4: Explosions

BACK to Ladder Collisions and Explosions

We have been using the conservation of momentum to model two objects in a collision. However, it can also be used to model explosions. When two objects explode, typically, the total momentum before the explosion is 0, and after the explosion the two objects move apart in different directions.

Whenever a gun or cannon is fired, it will be pushed backwards by the explosion. This is called the recoil. The speed at which it recoils is called the recoil velocity.

In each of the problems 1 - 6, the cannon and cannonball are not moving before the explosion. After the explosion, the cannonball moves forward and the cannon moves backwards. Define the positive direction as forwards and the negative direction as backwards. This means that the cannonball has POSITIVE velocity and momentum and the cannon has NEGATIVE velocity and momentum after the explosion.

  1. A cannon has a mass of 300 kg. It's operators load a cannonball with a mass of 30 kg. The cannon and the cannonball are stationary, when suddenly the cannon is fired! If the cannonball moves forward, with a velocity of 200 m/s, fill out the table below to figure out the speed at which the cannon recoils.
  2. A cannon has a mass of 400 kg. It's operators load a cannonball with a mass of 20 kg. The cannon and the cannonball are stationary, when suddenly the cannon is fired! If the cannonball moves forward, with a velocity of 100 m/s, fill out the table below to figure out the speed at which the cannon recoils.
  3. A cannon with a mass of 100 kg fires a cannonball with a mass of 20 kg. The cannon recoils with a speed of 15 m/s. With what speed was the cannonball fired?
  4. A cannon with a mass of 200 kg fires a cannonball with a mass of 5 kg. The cannon recoils with a speed of 4 m/s. With what speed was the cannonball fired?
  5. A cannon of unknown mass fires a 2 kg cannonball. The cannonball moves forwards with a speed of 100 m/s, and the cannon recoils backwards with a speed of 5 m/s. What is the mass of the cannon?
  6. A cannon with a mass of 400 kg fires a cannonball of unknown mass. The cannonball moves forwards with a speed of 80 m/s and the cannon moves backwards with a speed of 2 m/s. What is the mass of the cannonball?
  7. In problems 7 and 8, the the cannon was moving before the explosion. The recoil from its shot may make it speed up, or slow down, or even reverse direction!

  8. It is a period of civil war in a galaxy far far away. A flying space cannon is flying forwards at a speed of 20 m/s. The space cannon has a mass of 100 kg when it is not loaded, and the cannonball loaded inside has a mass of 10 kg. It fires the cannonball forwards with a speed of 400 m/s. After firing, what is the magnitude and direction of the velocity of the space cannon?
  9. A flying space cannon is flying forwards at a speed of 10 m/s. The space cannon has a mass of 160 kg when it is not loaded, and the cannonball loaded inside has a mass of 20 kg. It fires a cannonball backwards (the speed it is not flying) with a speed of 500 m/s. After firing, what is the magnitude and direction of the velocity of the space cannon?

Answers

Resources

This flipping physics video goes through the conceptual issues behind the conservation of momentum with explosions, and a provides mathematical proof of the conservation of momentum from Newton's Second Law.

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