A shell explodes into three fragments of equal masses.

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In summary, when a shell explodes into three equal fragments and two of them travel at right angles to each other with equal speeds, the third fragment will also have the same speed and will travel at an angle of 45 degrees to the original direction of the shell. This can be determined by using the conservation of momentum, where the total momentum due to several objects is equal before and after the explosion. The equation for the velocity of the third fragment is v3= root square of v^2(m1^2+m2^2) / m3, and the angle can be found using tan^-1 (m2/m1). By knowing that all the masses are equal, the final answer can be simplified to v3= sqrt(
  • #1
jasonbans
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Homework Statement


A shell explodes into three fragments of equal masses. If two fragments travel at right angles to one another with equal speeds, 'v', what is the direction and speed of the third fragment?


Homework Equations


doing ratios?


The Attempt at a Solution


i don't know what it mean by two fragments travel at right angles.
 
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  • #2


Travel at right angles means there is 90 degrees between their paths. For example, one might travel vertically, while the other travels horizontally.

For the question, think about what quantity will be conserved.
 
  • #3


BruceW said:
Travel at right angles means there is 90 degrees between their paths. For example, one might travel vertically, while the other travels horizontally.

For the question, think about what quantity will be conserved.

what does conserved really mean cause when i hear the word conserved i think of something being stored
 
  • #4


In physics, it roughly means 'stays the same'. Is this homework set by your teacher? Name me some quantities that you think might be conserved in this situation.
 
  • #5


p=mv?
 
  • #6


Yes, that's the one! You might also think of energy, but when the shell explodes it turns an unknown amount of chemical energy into kinetic energy, so energy conservation doesn't help us here.

So you're right to think of momentum conservation. After the shell explodes, there are 3 pieces, so you need to think of the equation for the total momentum due to several objects.
 
  • #7


BruceW said:
Yes, that's the one! You might also think of energy, but when the shell explodes it turns an unknown amount of chemical energy into kinetic energy, so energy conservation doesn't help us here.

So you're right to think of momentum conservation. After the shell explodes, there are 3 pieces, so you need to think of the equation for the total momentum due to several objects.

i got the velocity to be v2= root square of v^2(m1^2+m2^2) / m3

and the angle to be tan^-1 ( m2/m1)

am i right?
 
  • #8


jasonbans said:
i got the velocity to be v2= root square of v^2(m1^2+m2^2) / m3

and the angle to be tan^-1 ( m2/m1)

am i right?

The angle is right. I'm not totally sure I understand what your answer for the velocity is supposed to look like... Does it mean:
[tex]v_{third} = \frac{ \sqrt{v^2(m_1^2+m_2^2)} }{m_3} [/tex]
If this is what you meant, then yes, you've got this right as well.

The next step is to use the knowledge that all the masses are the same.
 
  • #9


ok thank you for the help!
 

1. What causes a shell to explode into three fragments of equal masses?

The explosion of a shell is typically caused by an explosive charge, which creates a sudden increase in pressure within the shell. This pressure causes the shell to break apart into smaller pieces, known as fragments.

2. Why do the fragments of a shell have equal masses?

The fragments of a shell typically have equal masses because the explosive charge is evenly distributed throughout the shell. This results in equal amounts of force being applied to all parts of the shell, causing it to break into equal pieces.

3. Is it possible for a shell to explode into unequal fragments?

While it is possible for a shell to explode into unequal fragments, it is less common. This can occur if the explosive charge is not evenly distributed, or if the shell is struck at a certain angle that causes it to break unevenly.

4. What factors can affect the mass distribution of the fragments?

The mass distribution of the fragments can be affected by various factors, such as the type and amount of explosive used, the angle and force of impact, and the structural integrity of the shell itself.

5. How does the equal mass distribution of the fragments impact the damage caused by the explosion?

The equal mass distribution of the fragments can impact the damage caused by the explosion in various ways. It can result in a more widespread and even distribution of the blast force, potentially causing less concentrated damage. However, it can also result in a larger overall area of damage due to the fragments being spread out more evenly.

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