Finding recoil velocity only given force and firing velocity

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Homework Help Overview

The problem involves determining the recoil velocity of a gun given the force exerted by a bullet, the weight of the gun, and the bullet's firing velocity. The context is rooted in concepts of impulse and momentum within classical mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss using impulse-momentum relations to relate force, mass, and change in velocity. There is an exploration of how to handle multiple unknowns, specifically mass and time, in the equations.

Discussion Status

Some participants have offered guidance on drawing free body diagrams and writing equations of motion. There is an ongoing exploration of the implications of the given weights and how they relate to mass, as well as the significance of the provided velocity.

Contextual Notes

Participants note the unusual weight values of the bullet and gun, which raises questions about their physical interpretation. The discussion also hints at the assumption that the scenario occurs near the Earth's surface, which may affect calculations related to mass.

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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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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).
 
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.
 
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.
 

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