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--- 183_notes:examples:deer_slug_example [2014/09/26 04:14] – created pwirving
+++ 183_notes:examples:deer_slug_example [2014/09/26 05:06] – pwirving
@@ Line 1: / Line 1: @@
 ===== Example: Firing a deer slug. =====
+How much force does a 12 gauge exert on your shoulder when firing a deer slug?
 === Facts ===
+Mass of gun = 3.5kg
+Mass of slug = 0.22kg
 === Lacking ===
+$\vec{F}_{net}$ on shoulder
 === Approximations & Assumptions ===
+${\Delta t} \longrightarrow  1/24s$ - 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.
+$\vec{V}_{Slug} \longrightarrow 500m/s$ This is a conservative estimate based on an internet search.
 === Representations ===
+System: Gun + Slug
+Surroundings: Nothing
+{{183_notes:examples:momentum_example_2_upload.jpg?600|}}
+$\vec{F}_{net} = \dfrac{\Delta\vec{p}}{\Delta t}$
+$\vec{p}_{sys,f} = \vec{p}_{sys,i}$
+$\vec{p}_{1,f} + \vec{p}_{2,f} = \vec{p}_{1,i} + \vec{p}_{2,i}$
+$m_1\vec{v}_{1,f} + m_2\vec{v}_{2,f} = m_1\vec{v}_{1,i} + m_2\vec{v}_{2,i}$
 === Solution ===
+${\Delta p_x} = 0$
+$P_{tot,x} = 0$
+Because
+$P_{tot,i,x} = 0$
+$0 = M_G * V_G + m_S * V_S \longrightarrow M_G * V_G$ is negative and $m_S * V_S$ is positive
+$V_G = {\dfrac{-m_s}{M_G}} V_S$
+$V_G = - {\dfrac{0.22kg}{3.5kg}}{500m/s} = -31.4m/s$
+Need to find what kind of force that is on your shoulder.
+$\vec{F}_{net} = \dfrac{\Delta\vec{p}}{\Delta t}$
+$\vec{F}_{net} =\dfrac{(3.5kg)(-31.4m/s + 0m/s)}{(1/24s)}$
+$\vec{F}_{net} = 2637.6N$ (at least)