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Lesson 41 – Collisions in Two Dimensions

Lesson 41 – Collisions in Two Dimensions. By: Fernando Morales September 25, 2013. Learning Goals. Recognize that momentum is a vector Familiarize with collisions involving high energy particles Solve problems related to elastic collisions in two-space. Professor R. S. Orr.

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Lesson 41 – Collisions in Two Dimensions

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  1. Lesson 41 – Collisions in Two Dimensions By: Fernando Morales September 25, 2013

  2. Learning Goals • Recognize that momentum is a vector • Familiarize with collisions involving high energy particles • Solve problems related to elastic collisions in two-space

  3. Professor R. S. Orr • Experimental High Energy Physics: The ATLAS Experiment at the CERN Large Hadron Collider • B.Sc.Imperial College, University of London, UK. (1968), Ph.D.Imperial College, University of London, UK. (1972), Post Doctoral, Rutherford Laboratory, UK. (1972-1974), University of Wisconsin, Madison, USA. (1974-1975), CERN Fellow and Staff Physicist, European Organization for Nuclear Research, Geneva (1976-1981), Research Scientist, Institute of Particle Physics (1981-1995),Visiting Scientist, CERN (1997-1998), JSPS Invitation Fellow, KEK - Japan (2005-2006), Fellow of American Physical Society (1995), Fellow of Royal Society of Canada (2009)

  4. X7 - 9 EXAMPLE Elastic Collision in 2D with Equal Masses Show that when 2 objects of equal mass collide obliquely (not head-on) and elastically, their subsequent paths are perpendicular Solution KEY: elastic collision  Kinetic Energy is Conserved For simplicity assume 1 mass is at rest before collision mv ² = mv1² + mv2² v² = v1² + v2² v1 v  v1 v2 v2 (by Pythagoras Theorem) Billiards 90 ° carom

  5. Collisions and Explosions – 2 Dimensions In all cases, Momentum is Conserved Momentum is a vector So the momentum in each direction is conserved X momentum before a collision or explosion = X momentum after the collision or explosion Y momentum before a collision or explosion = Y momentum after the collision or explosion

  6. X7 - 9 Collision in 2D A 5 kg blob of putty smashes into a 3 kg blob as shown; find vf (the collision is completely inelastic) EXAMPLE Solution 8 kg, ? m/s, ? º 5 kg, 6 m/s, 143 º Momentum is Conserved PF = PI PXF = PXI PYF = PYI 3 kg, 9 m/s, 270 º

  7. 2-D Collisions • An 8.0 kg mass collides elastically with a 5.0 kg mass that is at rest. Initially, the 8.0 kg mass was travelling to the right at 4.5 m/s. After the collision, it is moving with a speed of 3.65 m/s and at an angle of 27° to its original direction. What is the final speed and direction of motion for the 5.0 kg mass? Solution Link

  8. X7 - 10 EXAMPLE Find the missing data P is conserved m = 6 v = 30 m/s  = 45º In Y dir’n, P1Y = -P2Y v2 = -m1v1sin 45 / m2 sin (-60) v2 = 73.5 m/s In X dir’n, -P3X = P1X + P2X m3 = [m1v1cos 45 + m2v2 cos (-60)] / v3 m3 = 4 kg 3 2 1 m = ? v = 50 m/s  = 180º m = 2 kg v = ?  = - 60º

  9. Required Before Next Class • Pg. 253 # 1, 3, 4, 5, 6, 7

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