Finding recoil velocity only given force and firing velocity

In summary, The problem is asking for the recoil velocity of a gun that shoots a 50.0N bullet at a velocity of 200. m/s. The equation FΔt=mΔv can be used to solve this, but the mass of the gun is unknown. By setting up a Free-Body Diagram and using impulse-momentum relations, the equation F=mΔv/Δt can be used to solve for the unknown mass. However, the given weights may not be accurate, making the problem more challenging.
  • #1
junkmonk
2
0

Homework Statement


A 50.0N bullet leaves a 40.0N gun with a velocity of 200. m/s. What is the recoil velocity of the gun?


Homework Equations


I tried to figure this out by using anything in relation to FΔt = mΔv but, I'm left with two unsolved variables, Δt and m...
 
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  • #2
Draw a FBD for the gun and for the bullet and then write eqn of motion for each one (or impulse--momentum relations for each one).
 
  • #3
Okay, well I can write out the impulse relations on the FBD. Since FΔt=mΔv, then F=mΔv/Δt.
SO, putting m1Δv1/Δt = m2Δv2/Δt still leaves me with the mass unavailable, they don't cancel out since they're different... How do I solve this without the mass (or time)?

I'm just getting into impulse, the only impulse equation I've learned thus far IS FΔt=mΔv, so if there's any way that it can be solved using that or that with any other combination of simple linear motion equations, it would be best understood. But if there's no other way, than I'll definitely attempt to learn.

Thanks.
 
  • #4
This is all happening some where close to the surface of the earth, I presume? You were given weights, so masses should not be too difficult to find. Pretty strange weight values, however; that is one heavy bullet!

You need to think a bit about what velocity you are given.
 

1. How can I calculate the recoil velocity if I know the force and firing velocity?

The recoil velocity can be calculated using the formula vr = F/m, where vr is the recoil velocity, F is the force applied, and m is the mass of the object being fired.

2. Can I use this formula for any object being fired?

Yes, this formula can be used for any object as long as its mass is known and the force applied is constant. However, the resulting recoil velocity may differ depending on the mass and shape of the object.

3. Is there a difference in recoil velocity between different types of weapons?

Yes, the recoil velocity can vary between different types of weapons due to factors such as the mass of the bullet, the type of propellant used, and the design of the weapon. This formula can be used to calculate the recoil velocity for any weapon, but the resulting value may differ.

4. How does the angle at which the weapon is fired affect the recoil velocity?

The angle at which the weapon is fired does not affect the recoil velocity, as long as the force applied and the mass of the object remain constant. This formula only takes into account the force and mass, not the direction in which the object is fired.

5. Can this formula be used to calculate the recoil velocity of a moving object?

No, this formula is specifically for calculating the recoil velocity of an object being fired from a stationary position. For a moving object, the formula would need to take into account its initial velocity and momentum in addition to the force applied.

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