Conservation of Linear Momentum and kinetic energy of explosion

• peaceandlove
In summary, an object with a mass of 71 kg and a speed of 23 m/s explodes into two pieces, one 5 times as massive as the other. The explosion occurs in deep space and the less massive piece stops relative to the observer. Using the equations m1=5m2, (1/2)mv^2, and mv1 (initial) + mv2 (initial) = mv1 (final) + mv2 (final), the final kinetic energy of the smaller piece is calculated to be 3755.9 J.
peaceandlove

Homework Statement

An object, with mass 71 kg and speed 23 m/s relative to an observer, explodes into two pieces, one 5 times as massive as the other; the explosion takes place in deep space. The less massive piece stops relative to the observer. How much kinetic energy is added to the system during the explosion, as measured in the observer's reference frame?

Homework Equations

Equation 1: m1=5m2
Equation 2: (1/2)mv^2
Equation 3: mv1 (intiial) + mv2 (initial) = mv1 (final) + mv2 (final)

The Attempt at a Solution

I used equation 1 go determine the masses of the two exploded pieces and determined the initial kinetic energy by plugging in 71 kg and 23 m/s into equation 2. I then plugged in all the data into equation 3, where mv2 (final) is equal to 0, and solved for mv1 (final). I then plugged the final velocity for object 1, as well as the mass, into equation 2. When I subtracted the initial kinetic energy from the final kinetic energy, I came up with 93897.5 J.

Have to do conservation of momentum to find the speed of that heavier piece.
Only then can you calculate the KE after the explosion.

Oh, sorry, I guess that is just what you did! Did you get v = 27.6 for the bigger piece?

Oh! I think I know what I did wrong. For some reason I read that the LARGER piece stopped relative to the observer, but it's the SMALL piece that stops. In that case, wouldn't the answer be 3755.9 N? I got that by doing (1/2) times the mass of the larger piece times the final velocity of the larger piece. From that I subtracted (1/2) times the mass of the entire object before it exploded times the velocity of the entire object before it exploded.

Yes, I got 3755!

1. What is the conservation of linear momentum and kinetic energy of explosion?

The conservation of linear momentum and kinetic energy of explosion is a physical law that states that the total momentum and kinetic energy of a system before and after an explosion must remain constant. This means that the total momentum and kinetic energy of all objects involved in the explosion must be equal before and after the explosion.

2. How does the conservation of linear momentum and kinetic energy of explosion apply to real-world scenarios?

This law applies to real-world scenarios such as fireworks, car crashes, and rocket launches. In a firework explosion, the initial chemical energy is converted into kinetic energy, causing the fireworks to move in different directions while maintaining the same total momentum and kinetic energy. In a car crash, the total momentum and kinetic energy of the car and other objects involved must be equal before and after the collision.

3. What is the difference between linear momentum and kinetic energy?

Linear momentum is a measure of an object's motion, calculated by multiplying its mass by its velocity. Kinetic energy, on the other hand, is the energy an object possesses due to its motion, calculated by multiplying its mass by the square of its velocity. Linear momentum is a vector quantity, while kinetic energy is a scalar quantity.

4. How is the conservation of linear momentum and kinetic energy of explosion related to Newton's Laws of Motion?

The conservation of linear momentum and kinetic energy of explosion is related to Newton's Laws of Motion through the law of conservation of momentum. This states that in a closed system, the total momentum of all objects must remain constant. This is in line with Newton's Third Law, which states that for every action, there is an equal and opposite reaction.

5. Can the conservation of linear momentum and kinetic energy of explosion be violated?

No, the conservation of linear momentum and kinetic energy of explosion is a fundamental law of physics and cannot be violated. Any violation would indicate a flaw in the measurement or calculation process. However, in an open system, such as an explosion in space, there may be external forces that can change the total momentum and kinetic energy of the system.

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