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Momentum and Collisions Russ Ballard Kentlake Science Department April 22, 2003 Linear Momentum • Objective – be able to compute linear momentum and components of momentum. April 22, 2003 Kentlake Science Department 2 One particle systems • Linear momentum is the product • • April 22, 2003 of the mass and the velocity. = mv units = kg m/s it is a vector quantity in the same direction as the velocity. Kentlake Science Department 3 More than one particle • Total linear momentum is the total momentum of the system total = 1 + 2 + 3 + … = ii April 22, 2003 Kentlake Science Department 4 Example 6.1 Momentum: Mass and Velocity A 100 kg player runs straight down the field with a velocity of 4.0 m/s. A 1.0 kg artillery shell leaves the barrel of a gun with a muzzle velocity of 500 m/s. Which has the greater momentum? April 22, 2003 Kentlake Science Department 5 Follow-up • What would the speed of the football payer need to have the same momentum? April 22, 2003 Kentlake Science Department 6 Total momentum: a vector sum • What is the total sum for each of the systems of particles (2systems). April 22, 2003 Kentlake Science Department 7 System One = 5.0 kgm/s 2 = 3.0 kgm/s 1 = 2.0 kgm/s Total Individual momentum momenta of system April 22, 2003 Kentlake Science Department 8 System Two 53° 3 = 4.0 kgm/s y = 4.0 kgm/s 2 = -8.0 kgm/s x = -3.0 kgm/s1 = 5.0 kgm/s Total Individual momentum momenta of system April 22, 2003 Kentlake Science Department 9 The Conservation of Linear Momentum • Objective – to be able to • Explain the conditions for the conservation of linear momentum • Apply it to physical conditions April 22, 2003 Kentlake Science Department 10 Example 6.4 Before and After: considerations of Momentum • Two masses m1 = 1.0kg and m2 = 2.0kg, are held on either side of a light compressed spring by a string joining them. The string is burned and the masses move apart on a frictionless surface, with m1 having a velocity of 1.8 m/s to the left. What is the velocity of m2? April 22, 2003 Kentlake Science Department 11 Example 6.6 a glancing collision: components of momentum • A moving shuffleboard puck has a glancing collision with a stationary one of the same mass. Considering friction to be negligible, what are the speeds of the pucks after the collision? April 22, 2003 Kentlake Science Department 12 Path of Collision Vi = .95m/s 50° 40° April 22, 2003 Kentlake Science Department 13 Impulse • Objective to be able to relate • Impulse and momentum • Kinetic energy and momentum April 22, 2003 Kentlake Science Department 14 Impulse • Objects in contact exert force on each other. • If you consider average force, Newton’s Laws help. Ft = = f -I Impulse = Ft April 22, 2003 Kentlake Science Department 15 Impulse • If you increase the time you decrease the impulse. • Jump from height. • Catch a ball. • Air bag. April 22, 2003 Kentlake Science Department 16 Impulse • Applied impulse. • Following through • Increase contact time • Increases force applied • Improve control April 22, 2003 Kentlake Science Department 17 Example 6.7 teeing off: the impulse-momentum theorem • A golfer drives a .10-kg ball from an elevated tee, giving it an initial horizontal speed of 40m/s (about 90mph). The club and the ball are in contact for 1.0 ms (millisecond). What is the average force exerted by the club on the ball during this time? April 22, 2003 Kentlake Science Department 18 Impulse • A collision is an exchange of momentum and energy. • KE = ½ mv2 = April 22, 2003 (mv) 2 2m Kentlake Science Department = ρ2 2m 19 Elastic and Inelastic Collisions • Objective to be able to describe the conditions on kinetic energy and momentum in elastic and inelastic collisions April 22, 2003 Kentlake Science Department 20 Elastic Collisions • Kinetic energy is conserved. • Some is transformed to potential during the collision. • Object is elastic it returns to original shape. April 22, 2003 Kentlake Science Department 21 Inelastic Collisions • Kinetic energy is not conserved. • Object do not return to original shape. • Isolated systems momentum is always conserved. April 22, 2003 Kentlake Science Department 22 Center of Mass • Objective to be able to • Explain the concept of the center of mass and compute its location for simple systems • Describe how the center of mass and center of gravity are related April 22, 2003 Kentlake Science Department 23 Example 6.12 Finding the Center of Mass: a Summation • Example 6.13 a Dumbbell: Center of Mass Revisited April 22, 2003 Kentlake Science Department 24 Jet Propulsion and Rockets • Objective to apply the conservation of momentum in the explanation of jet propulsion and the operation of rockets April 22, 2003 Kentlake Science Department 25 Important concepts • = mv • total = 1 + 2 + 3 + … = ii • F = /t • Impulse = Ft = = mv-mvo April 22, 2003 Kentlake Science Department 26 Conservation of Momentum Perfect inelastic collision m1v1i + m2v2i = (m1+ m2)vf Elastic collision m1v1i + m2v2i = m1v1f + m2v2f April 22, 2003 Kentlake Science Department 27 Elastic vs. Inelastic • Elastic • f = i • Kf = Ki • Inelastic • f = i • Kf < Ki April 22, 2003 Kentlake Science Department 28 The center of mass • Is the point at which all of the • April 22, 2003 mass of am object or system may be considered to be connected. (The center of gravity is the point where all the weight may be considered to be concentrated. XCM = Kentlake Science Department 29