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## Aim: What is the law of conservation of momentum?

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**Aim: What is the law of conservation of momentum?**Do Now: A 20 kg object traveling at 20 m/s stops in 6 s. What is the change in momentum? Δp = mΔv Δp = m(vf – vi) Δp = (20 kg)(0 m/s – 20 m/s) Δp = -400 kg·m/s**Newton’s cradle demo**How can we explain what is going on? The momentum of: one goes in, one goes out two goes in, two goes out etc.**The Law of Conservation of Momentum**The momentum of any closed, isolated system does not change.**A 2,000 kg car traveling north at 3 m/s strikes a 3,000 kg**car traveling south at 2 m/s. What is the final momentum after the cars collide? pi = pf p1i + p2i = pf mv1i + mv2i = pf (2,000 kg)(3 m/s) + (3,000 kg)(-2 m/s) = pf 6,000 kg·m/s – 6,000 kg·m/s = pf pf = 0 kg·m/s**Spring or Gun**When firing a gun, there will always be a recoil due to momentum being conserved http://www.youtube.com/watch?v=sTHPfz0bVycA 5 kg gun fires a 0.02 kg bullet. If the bullet exits the gun at 800 m/s East, calculate the recoil velocity of the gun. Rifle Recoil Video**Inelastic Collision**A collision where the objects stick together after the collision • Masses combine • Velocity decreases after the collision**A 1 kg cart traveling at 1 m/s to the right strikes a 0.7 kg**cart initially at rest. After the collision, the two stick together. Calculate the final velocity of the two cart system. pi = pf p1i + p2i = p(1+2)f mv1i + mv2i = (m1 + m2)vf (1 kg)(1 m/s) + (0.7 kg)(0 m/s) = (1 kg + 0.7 kg)vf 1 + 0 = 1.7vf 1 = 1.7vf vf = 0.59 m/s right**Elastic Collision**Collision where the objects bounce off each other**Mass 1 (1 kg) is traveling at 1 m/s to the right and strikes**mass 2 (1 kg) that is at rest. After the collision, mass 1 is at rest. What is the velocity of the mass 2? pi = pf p1i + p2i = p1f + p2f m1v1i + m2v2i = m1v1f + m2v2f (1 kg)(1 m/s) + (1 kg)(0 m/s) = (1 kg)(0 m/s) +(1 kg)v2f 1 + 0 = 0 + 1v2f v2f = 1 m/s right**What if a heavier objects strikes a lighter object?**• Both will continue to move in the same direction • The heavier object will slow down**Mass 1 (1 kg) is traveling at 1 m/s to the right and strikes**mass 2 (0.7 kg) that is at rest. After the collision, mass 1 is traveling at 0.18 m/s to the right. What is the velocity of the mass 2? pi = pf p1i + p2i = p1f + p2f m1v1i + m2v2i = m1v1f + m2v2f (1 kg)(1 m/s) + (0.7 kg)(0 m/s) = (1 kg)(0.18 m/s) +(0.7 kg)v2f 1 + 0 = 0.18 + 0.7v2f 0.82 = 0.7v2f v2f = 1.17 m/s right**What if a lighter object strikes a heavier object?**• The lighter object will bounce off in the opposite direction**Mass 1 (1 kg) is traveling at 1 m/s to the right and strikes**mass 2 (1.4 kg) that is at rest. After the collision, mass 2 is traveling at 0.83 m/s to the right. What is the velocity of the mass 1? pi = pf p1i + p2i = p1f + p2f m1v1i + m2v2i = m1v1f + m2v2f (1 kg)(1 m/s) + (1.4 kg)(0 m/s) = (1 kg)v1f +(1.4 kg)(0.83 m/s) 1 + 0 = v1f + 1.2 v1f = -0.2 m/s or 0.2 m/s left