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183_notes:examples:deer_slug_example [2014/09/26 04:14] – created pwirving | 183_notes:examples:deer_slug_example [2014/10/01 05:20] – pwirving | ||
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===== Example: Firing a deer slug. ===== | ===== Example: Firing a deer slug. ===== | ||
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+ | How much force does a 12 gauge exert on your shoulder when firing a deer slug? | ||
=== Facts === | === Facts === | ||
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+ | Mass of gun = 3.5kg | ||
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+ | Mass of slug = 0.22kg | ||
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=== Lacking === | === Lacking === | ||
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+ | $\vec{F}_{net}$ on shoulder | ||
=== Approximations & Assumptions === | === Approximations & Assumptions === | ||
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+ | ${\Delta t} \longrightarrow | ||
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+ | $\vec{V}_{Slug} \longrightarrow 500m/s$ This is a conservative estimate based on an internet search. | ||
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=== Representations === | === Representations === | ||
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+ | System: Gun + Slug | ||
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+ | Surroundings: | ||
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+ | {{183_notes: | ||
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+ | $\vec{F}_{net} = \dfrac{\Delta\vec{p}}{\Delta t}$ | ||
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+ | $\vec{p}_{sys, | ||
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+ | $\vec{p}_{1, | ||
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+ | $m_1\vec{v}_{1, | ||
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=== Solution === | === Solution === | ||
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+ | 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. | ||
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+ | ${\Delta p_x} = 0$ | ||
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+ | The total momentum of the system in x direction is also 0. | ||
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+ | $P_{tot,x} = 0$ | ||
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+ | This is because the initial momentum of the system is 0 and therefore the final momentum of the system is zero. | ||
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+ | $P_{tot, | ||
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+ | We can relate the momentum before to the momentum after then giving us the following equation. | ||
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+ | $0 = M_G * V_G + m_S * V_S \longrightarrow M_G * V_G$ is negative and $m_S * V_S$ is positive | ||
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+ | $V_G = {\dfrac{-m_s}{M_G}} V_S$ | ||
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+ | $V_G = - {\dfrac{0.22kg}{3.5kg}}{500m/ | ||
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+ | Need to find what kind of force that is on your shoulder. | ||
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+ | $\vec{F}_{net} = \dfrac{\Delta\vec{p}}{\Delta t}$ | ||
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+ | $\vec{F}_{net} =\dfrac{(3.5kg)(-31.4m/ | ||
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+ | $\vec{F}_{net} = 2637.6N$ (at least) | ||
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