Explosion mass and magnitude physics

• sam_amy
In summary: The third is the direction and magnitude of the vector sum. So you could say that the final momentum of the system is: ##\vec p=\vec{m_{1}+\vec{m_{2}}+\vec{m_{3}}=16.5 kg\vec{v}##
sam_amy
An object with total mass mtotal = 16.5 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.7 kg moves up and to the left at an angle of θ1 = 19° above the –x axis with a speed of v1 = 26.5 m/s. A second piece with mass m2 = 5.2 kg moves down and to the right an angle of θ2 = 24° to the right of the -y axis at a speed of v2 = 21.2 m/s.

What is the magnitude of the final momentum of the system (all three pieces)?
What is the mass of the third piece?
What is the x-component of the velocity of the third piece?

So I don't even know where to begin with this...
In class we went over Kinetic Energy of a system but not for momentum...Would it just be the sum of the masses times the sum of the velocities...? I don't know m3 or v3 though :(

That would be the expression for momentum, but the idea here is to use the conservation of momentum. An explosion always means some internal process, so something that is not external to the system. If you look at the momentum of the object before the explosion, then it must be equal to the momentum after the explosion since there are no net external forces acting on the object, only the internal ones due to the explosion.

1 person
So I don't even know where to begin with this...
Well, you could start with the second question. Shouldn't be too hard to calculate the mass of the third piece

Then:
momentum...Would it just be the sum of the masses times the sum of the velocities...?
No. momentum is per "piece. It is the vector that has to do with amount of motion, hence mass times velocity vector": ##\vec p=m\vec v##

1 person
Ok yes, I've figured out how to do the first two, but how do I figure out the components?

The center of mass is sitting still before the explosion. The three fragments fly off all over the place, but the center of mass still sits still, because of action = - reaction. That means the three momentum vectors add up to a vector of zero length. You have two of the three.

1. What is the difference between mass and magnitude in explosions?

Mass refers to the amount of matter involved in an explosion, while magnitude refers to the strength or intensity of the explosion. Mass is typically measured in kilograms, while magnitude is measured on a scale such as the Richter scale.

2. How is the mass of an explosion determined?

The mass of an explosion is determined by measuring the total amount of explosive material involved. This can be done by weighing the explosives before detonation or by calculating the amount of energy released during the explosion.

3. What factors affect the magnitude of an explosion?

The magnitude of an explosion is affected by several factors, including the amount and type of explosive material, the confinement of the explosion, and the location of the explosion. In general, larger amounts of more powerful explosives will result in a higher magnitude explosion.

4. How are explosions classified by magnitude?

Explosions are typically classified by magnitude using a scale, such as the Richter scale for earthquakes or the Modified Mercalli scale for volcanic eruptions. These scales measure the effects of the explosion, such as damage to structures and the intensity of shaking.

5. Can the magnitude of an explosion be predicted?

The magnitude of an explosion can be estimated based on the amount and type of explosive material used, as well as other factors such as the location and confinement of the explosion. However, it is difficult to accurately predict the exact magnitude of an explosion due to the complex nature of explosive reactions.

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