Conservation of mass with fireworks

In summary, the conversation discusses a problem involving a 3.0 kg rocket exploding into three equal pieces, with piece A moving horizontally at a speed of 4 km/hr and piece B moving at a 37 degree angle downward from the horizontal at a speed of 5 km/hr. The question is posed about the magnitude and direction of the velocity of piece C, with the suggestion to use conservation of momentum to solve the problem. The conversation ends with a suggestion to write out two equations with two unknowns, the velocity and direction of piece C.
  • #1
KingNothing
882
4
Hi. This was the one extra problem credit problem I couldn't figure out in our momentum unit. (Since its not homework I posted here)

In a fireworks display, a 3.0 kg rocket moving at 4 km/h straight up explodes into three equal pieces of of 1.0 kg in mass. Piece A moves straight horizontally at a speed of 4 km/hr. Piece B moves at 37 degrees down from the horizontal and opposite piece A at a speed of 5 km/hr.

What is the magnitude and direction of the velocity of piece C?

My ideas: Well, since there's conservation of mass we know the velocity.

Can someone work this out for me?
 
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  • #2
Can you assume that the momentum is preserved? If so then it's just:
[tex]M_TV_0 = m_1v_1 + m_2v_2 + m_3v_3[/tex]
Write that for two axes, X and Y, and separate the velocity vectors as well. You will have two equations with two unknowns. The unknowns would be the 3rd piece's velocity and the angle (direction) of that velocity.
 

1. How is the conservation of mass demonstrated in fireworks?

The conservation of mass is demonstrated in fireworks through the chemical reactions that take place. The reactants, which include gunpowder and other chemicals, have a certain mass. As these reactants undergo combustion, they release energy and form new products. However, the total mass of the products is equal to the total mass of the reactants, showing that mass is conserved.

2. Can the conservation of mass be observed in the colors of fireworks?

Yes, the conservation of mass can also be observed in the colors of fireworks. The different colors are produced by different chemical compounds, and the mass of these compounds remains constant throughout the reaction. This means that the total mass of the reactants is still equal to the total mass of the products, even though the colors may appear to be different.

3. How does the conservation of mass affect the size and shape of fireworks?

The conservation of mass does not directly affect the size and shape of fireworks. The size and shape are determined by the design and construction of the firework itself. However, the conservation of mass does play a role in the trajectory and movement of the firework, as the mass of the reactants affects the force and thrust produced.

4. Are there any exceptions to the conservation of mass in fireworks?

There are no exceptions to the conservation of mass in fireworks. As long as the reactions are happening in a closed system, the total mass will always remain constant. However, there may be some minor discrepancies due to factors such as evaporation or loss of small particles during the explosion.

5. How is the conservation of mass important in the safety of using fireworks?

The conservation of mass is important in the safety of using fireworks because it ensures that the reactions are predictable and controlled. If there were any major deviations from the conservation of mass, it could result in unexpected explosions or dangerous chemical reactions. By understanding and applying the principle of conservation of mass, firework manufacturers can create safe and enjoyable displays for everyone to enjoy.

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