Gun-projectile Elastic Collisions

I'm reading my textbook and there's a problem asking what the muzzle speed of a projectile would be if the gun it is being fired from is free to recoil. I'm given the muzzle speed of the projectile when the gun is stationary, the mass of the projectile, and the mass of the gun. I'm also told that the kinetic energies of the system is the same for both cases. How is a problem like this solved?In summary, the problem requires using momentum and kinetic energy to solve for the muzzle speed of the projectile when the gun is free to recoil. This can be done by setting up two simultaneous equations and solving for the unknown velocity.
  • #1
Calvin Pitts
So I'm reading my textbook and there's a problem asking what the muzzle speed of a projectile would be if the gun it is being fired from is free to recoil. I'm given the muzzle speed of the projectile when the gun is stationary, the mass of the projectile, and the mass of the gun. I'm also told that the kinetic energies of the system is the same for both cases. How is a problem like this solved? Every equation I've thought of so far ends up with two variables (the projectile's new speed and the gun's free-to-recoil speed).
 
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  • #2
Calvin Pitts said:
So I'm reading my textbook and there's a problem asking what the muzzle speed of a projectile would be if the gun it is being fired from is free to recoil. I'm given the muzzle speed of the projectile when the gun is stationary, the mass of the projectile, and the mass of the gun. I'm also told that the kinetic energies of the system is the same for both cases. How is a problem like this solved? Every equation I've thought of so far ends up with two variables (the projectile's new speed and the gun's free-to-recoil speed).
Welcome to the PF. :smile:

When there are no outside forces involved (when the gun is free to recoil), what fundamental quantities are conserved?
 
  • #3
berkeman said:
Welcome to the PF. :smile:

When there are no outside forces involved (when the gun is free to recoil), what fundamental quantities are conserved?
Momentum is conserved.
 
  • #4
BTW, once you get the fundamental concepts involved, you can start a thread about the problem in the Homework Help, Introductory Physics forum, and fill out the Template that you are provided there. You can show your work on the problem, and ask us to check it for you. :smile:
 
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  • #5
berkeman said:
BTW, once you get the fundamental concepts involved, you can start a thread about the problem in the Homework Help, Introductory Physics forum, and fill out the Template that you are provided there. You can show your work on the problem, and ask us to check it for you. :smile:
Awesome, thanks for letting me know!
 
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  • #6
Calvin Pitts said:
Momentum is conserved.
Great! So go ahead and start the thread in the HH forums, and show how you work out the problem using that information. Go ahead and post a link to your new thread here once you've started it.
 
  • #7
Create one equation using momentum, and another with kinetic energy.
 
  • #8
scottdave said:
Create one equation using momentum, and another with kinetic energy.
Good hints. Let's see what he posts in his HH thread. Thanks.
 
  • #9
berkeman said:
Good hints. Let's see what he posts in his HH thread. Thanks.
I'm spending as much time trying to figure out how to post on the thread as I am trying to figure out the problem. Haha I'm using an iPhone right now, which always seems to make my life harder :)
 
  • #10
Oh rats. There may be a bug that keeps you from being able to post in the Homework Help forums using the PF app right now, sorry about that.. Can you post from a laptop or desktop later, or just use the web to post it? Ack!
 
  • #11
berkeman said:
Oh rats. There may be a bug that keeps you from being able to post in the Homework Help forums using the PF app right now, sorry about that.. Can you post from a laptop or desktop later, or just use the web to post it? Ack!
I'm actually just using the web browser on my phone. Haha I think I can post, it just takes a while to get there. I'm having more trouble figuring out the problem now. Because I'm not exactly sure how to relate momentum and kinetic energy.
 
  • #12
Calvin Pitts said:
. Because I'm not exactly sure how to relate momentum and kinetic energy.
The hint was to use those for two simultaneous equations...
 
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  • #13
I'll go ahead and close this thread in the technical forums so you can start your thread in the Homework Help forums. :smile:
 
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1. What is a gun-projectile elastic collision?

A gun-projectile elastic collision refers to the interaction between a gun and a projectile (such as a bullet or a pellet) where both objects collide and rebound without any loss of kinetic energy. In other words, the total kinetic energy of the system remains constant before and after the collision.

2. How do you calculate the velocities of the gun and projectile after the collision?

The velocities of the gun and projectile after the collision can be calculated using the conservation of momentum and conservation of kinetic energy equations. The equations take into account the masses and velocities of both objects before and after the collision.

3. What factors can affect the outcome of a gun-projectile elastic collision?

The most significant factor that can affect the outcome of a gun-projectile elastic collision is the relative masses and velocities of the gun and projectile. Other factors such as the angle of collision, the elasticity of the objects, and external forces (such as air resistance) can also have an impact on the outcome.

4. Can a gun-projectile elastic collision result in a perfectly elastic collision?

Yes, it is possible for a gun-projectile elastic collision to result in a perfectly elastic collision, where the objects rebound with the same velocity as before the collision. This would occur if there is no loss of kinetic energy due to external factors and the objects have an elastic collision coefficient of 1.

5. What are some real-world examples of gun-projectile elastic collisions?

Some common examples of gun-projectile elastic collisions include shooting a bullet from a gun, firing a paintball from a paintball gun, and shooting a pellet from an air gun. These collisions also occur in sports such as billiards, where the cue ball collides with other balls on the table.

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