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lecture13

# lecture13 - Momentum Tuesday Demo Skateboard Ramp Tuesday...

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Unformatted text preview: Momentum Tuesday, November 16, 2010 Demo Skateboard Ramp Tuesday, November 16, 2010 Newton’s Third Law From Newton: “To every action there is always opposed an equal reaction; or, the mutual actions of two objects upon each other are always equal, and directed to contrary parts.” Tuesday, November 16, 2010 Newton’s Third Law Commonly phrased as: “For every action there is an equal but opposite reaction.” ￿ ￿ FA on B = −FB on A Tuesday, November 16, 2010 Demo Drop Small on Large Ball Tuesday, November 16, 2010 Newton’s Third Law ￿ ￿ FA on B = −FB on A Tuesday, November 16, 2010 Newton’s Third Law ￿ ￿ FA on B = −FB on A mB￿ B = −mA￿ A a a ∆￿B v ∆￿A v mB = −mA ∆t ∆t ∆(mB ￿B ) v ∆(mA￿A ) v =− ∆t ∆t Tuesday, November 16, 2010 Momentum p = m￿ ￿ v Tuesday, November 16, 2010 Momentum Tuesday, November 16, 2010 Demo Newton’s Cradle Tuesday, November 16, 2010 Momentum p = m￿ ￿ v Tuesday, November 16, 2010 Momentum & Force ￿ v ￿ = lim ∆(m￿ ) F ∆t→0 ∆t ￿ ￿ = lim ∆p F ∆t→0 ∆t ￿ Tuesday, November 16, 2010 Total Momentum Momentum is a vector! p = m￿ ￿ v Tuesday, November 16, 2010 Total Momentum Momentum adds like a vector! ￿￿ P = pA + pB + pC + ... ￿ ￿ Tuesday, November 16, 2010 College Physics: Motion along a Straight Line A space capsule follows a circular orbit around a planet. A shaped charge blows the capsule into two fragments. As shown in the figure, one fragment falls straight toward the planet's surface. How does the other fragment move right after the explosion? A. It continues on the circular orbit of the original capsule. B. It moves straight away from the planet. C. It moves up and to the right. Tuesday, November 16, 2010 College Physics: Motion along a Straight Line A space capsule follows a circular orbit around a planet. A shaped charge blows the capsule into two fragments. As shown in the figure, one fragment falls straight toward the planet's surface. How does the other fragment move right after the explosion? C. It moves up and to the right. Tuesday, November 16, 2010 Recall... Internal vs. External Forces Isolated Systems Tuesday, November 16, 2010 Conservation of Momentum The total momentum of a system is constant whenever the vector sum of the external forces on the system is zero. In particular, the total momentum of an isolated system is constant. Tuesday, November 16, 2010 Total Momentum Momentum adds like a vector! ￿￿ P = pA + pB + pC + ... ￿ ￿ Tuesday, November 16, 2010 Tuesday, November 16, 2010 Tuesday, November 16, 2010 Tuesday, November 16, 2010 Example... A marksman holds a 3.00 kg rifle loosely, allowing it to recoil freely when fired, and fires a bullet of mass 5.00 g horizontally with a speed vB = 300 m/s. What is the recoil speed vR of the rifle? What are the final kinetic energies of the bullet and the rifle? Tuesday, November 16, 2010 Collisions Tuesday, November 16, 2010 Collisions Elastic Collisions Conservative Forces Kinetic Energy is Conserved Inelastic Collisions Kinetic Energy is Lost! Tuesday, November 16, 2010 Inelastic Collisions Tuesday, November 16, 2010 Inelastic Collisions pi = p f ￿ ￿ K i > Kf Tuesday, November 16, 2010 Completely Inelastic Collisions Objects stick together after collision. Tuesday, November 16, 2010 Completely Inelastic Collisions Objects stick together after collision. pi = p f ￿ ￿ m1￿1,i + m2￿2,i = (m1 + m2 )￿f v v v m1￿1,i + m2￿2,i v v ￿f = v (m1 + m2 ) Tuesday, November 16, 2010 Example... Tuesday, November 16, 2010 Demo Elastic vs. Inelastic Tuesday, November 16, 2010 Elastic Collisions Tuesday, November 16, 2010 Elastic Collisions pi = p f ￿ ￿ Ki = Kf Tuesday, November 16, 2010 Demo ollisions on an Air Track Tuesday, November 16, 2010 ...
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