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## Conservation of Momentum

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**Conservation of Momentum**Why does my shoulder hurt after I shoot my hunting rifle?**Conservation of Momentum**• pi = pf • In the absence of net external forces acting on the objects, momentum is conserved • Net force provides an impulse, which would result in momentum changing**Conservation of Momentum**pai = m(v) pbi = m(0) pbf = m(v) paf = m(0)**Conservation of Momentum**• Momentum is conserved for all objects in the interaction, even if one doesn't stop pai + pbi = paf + pbf**Is momentum conserved here?**Yes, due to the vector nature of momentum.**Is momentum conserved?**A B • Initial velocities of both objects is 0. • pai = ma(0) • pbi = mb(0) • Σpi = 0**Is momentum conserved?**A B • paf = ma(-va) • pbf = mb(vb) • pf = 0 • Σpi = Σpf, so momentum is conserved!! pf = ma(-va) + mb(vb)**Why do internal forces result in momentum being conserved?**• When Girl A pushes on Girl B, according to Newton’s 3rd Law, Girl B pushes on Girl A • How much? • These forces are equal in magnitude and opposite in direction • The time over which these forces act is exactly the same • Only while the girls are in contact, in this case**Why do internal forces result in momentum being conserved?**• Impulse is equal in magnitude but opposite in direction • I = (ΣF)(Δt) • Forces are equal and opposite, times are equal • Δp is equal in magnitude, opposite in direction, resulting in Σp = 0!!**How does the gun work?**• Only forces are internal (no net external forces are adding impulse to the system) • The momentum of both will add up to zero (bullet is +, gun is -)