183_notes:examples:deer_slug_example

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Next revision		 Previous revision
183_notes:examples:deer_slug_example [2014/09/26 04:14] – created pwirving183_notes:examples:deer_slug_example [2014/10/01 05:24] (current) – pwirving
Line 1: Line 1:
 ===== Example: Firing a deer slug. ===== ===== Example: Firing a deer slug. =====
 +
 +How much force does a 12 gauge exert on your shoulder when firing a deer slug?
  
 === Facts === === Facts ===
 +
 +Mass of gun = 3.5kg
 +
 +Mass of slug = 0.22kg
 +
  
 === Lacking === === Lacking ===
 +
 +→Fnet on shoulder
  
 === Approximations & Assumptions === === Approximations & Assumptions ===
 +
 +Δt⟶1/24s - Based on when a gun is fired in a movie, it usually occurs at about one movie frame, therefore, the collision time is less than 1/24s.
 +
 +→VSlug⟶500m/s This is a conservative estimate based on an internet search.
 +
  
 === Representations === === Representations ===
 +
 +System: Gun + Slug
 +
 +Surroundings: Nothing
 +
 +{{183_notes:examples:momentum_example_2_upload.jpg?600|}}
 +
 +→Fnet=Δ→pΔt
 +
 +→psys,f=→psys,i
 +
 +→p1,f+→p2,f=→p1,i+→p2,i
 +
 +m1→v1,f+m2→v2,f=m1→v1,i+m2→v2,i
 +
  
 === Solution === === Solution ===
 +
 +We know that the momentum of the system (gun + slug) does not change due to their being no external forces acting on the system, therefore, the change in momentum in the x-direction is 0.
 +
 +Δpx=0
 +
 +The total momentum of the system in x direction is also 0.
 +
 +Ptot,x=0
 +
 +This is because the initial momentum of the system is 0 and therefore the final momentum of the system is zero.
 +
 +Ptot,i,x=0
 +
 +We can relate the momentum before to the momentum after then giving us the following equation.
 +
 +0=MG∗VG+mS∗VS⟶MG∗VG is negative and mS∗VS is positive (see diagram).
 +
 +To find the force acting on the shoulder of the shooter me need to know VG in order to find change in momentum for the gun and relate this to the force using →Fnet=Δ→pΔt. Rearrange the previous equation.
 +
 +VG=−msMGVS
 +
 +Fill in the values for the corresponding variables.
 +
 +VG=−0.22kg3.5kg500m/s=−31.4m/s
 +
 +Use the value found for VG to find the change in momentum and hence find what kind of force that is on your shoulder.
 +
 +→Fnet=Δ→pΔt
 +
 +Fill in values for known variables.
 +
 +→Fnet=(3.5kg)(−31.4m/s+0m/s)(1/24s)
 +
 +→Fnet=2637.6N (at least)
 +
 +
 +
 +
  • 183_notes/examples/deer_slug_example.1411704889.txt.gz
  • Last modified: 2014/09/26 04:14
  • by pwirving