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Linear Momentum 5-1 Linear Momentum Linear Momentum, p – defined as mass x velocity p mv The unit is kg·m/s A quantity used in collisions So a small object with a large velocity could have the same momentum as a large object with a small velocity 9-1 Linear Momentum 5.2 Momentum and Newton’s Second Law Newton’s Second Law is F ma This is only true for objects with a constant mass The original form of the equation was p F t This statement is true even if the mass varies 5.2 Momentum and Newton’s Second Law 5.3 Impulse A baseball player hits a pitch Bat delivers an impulse We actually only consider average force Impulse is define as Ft p 5.3 Impulse An increase in time produces a decreases in force Airbag A decrease in time produces an increase in force 5.3 Impulse 5.4 Conservation of Linear Momentum If no net external force is applied to a system Then momentum is conserved p0 p 5.4 Conservation of Linear Momentum External Forces will result in a change in momentum, so no conservation 1.Force added in Shuttle Launch 2.Force removed 5.4 Conservation of Linear Momentum 5.5 Inelastic Collisions Inelastic collision – momentum is conserved, but energy is lost Momentum is conserved p0 p mAv A0 mB vB 0 mAv A mB vB 5.5 Inelastic Collisions Completely (or perfectly) Inelastic collision – two objects collide and stick together mAv A0 mB vB 0 (mA mB )v 5.5 Inelastic Collisions Example: On a touchdown attempt, a 95 kg running back runs toward the end zone at 3.75 m/s. A 111kg linebacker moving at 4.10 m/s meets the runner in a head on collision. If the two players stick together what is their velocity immediately after the collision? mAv A0 mB vB 0 (mA mB )v (95)(3.75) (111)( 4.10) (95 111)v v 0.48 ms 5.5 Inelastic Collisions If the collision occurs in two dimensions We need to consider the x and y axis separately mAv A0 x mB vB0 x (mA mB )vx mAvA0 y mBvB0 y (mA mB )v y 5.5 Inelastic Collisions Then we use vector addition to calculate the magnitude and velocity. v v v 2 x 2 y vy tan vx 1 5.5 Inelastic Collisions Example: A 950kg car traveling east at 16m/s collides with a 1300 kg car traveling north at 21 m/s. If the collision is completely inelastic, what is the magnitude and direction of the cars’ velocity after the collision? mAvA0 xy mB vB00xy (mAA mBB )vxy 2 2 )( 16 ) ( 1300 )( 0 ) ( 950 1300 ) v v(950 6 . 76 m / s v 6 . 76 12 . 1 13.9 ms x 2 2 x v v v x y v(v950 6 . 76 m / s x )( 120.)1m(1300 / s )( 21) (950 1300)v y tan 1 12.1 60.8o y v y 12.1m / s vy tan x vCollisions 5.5 Inelastic 1 6.76 5.6 Elastic Collisions Elastic collision – two objects collide and bounce apart Elastic Collisions Momentum is conserved m Av A0 mB vB0 m Av A mB vB Kinetic energy is conserved too 1 2 mv mv mv mv 2 A A0 1 2 2 B B0 1 2 2 A A 5.5 Elastic Collisions 1 2 2 B B A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? m Av A0 mB vB0 m Av A mB vB (10)(2)20 (510 )(0v)A10 5vvBA 5vB 1 2 1 2 mv mv mv mv 2 A A0 1 2 2 B B0 1 2 2 A A 1 2 2 B B (10 (10 )()( 2)2)40 (5 )(10 0) v (10 (5)v(5)v 5(10 v)v)v 2 2 1 2 2 2 1 A 2 2 2 2 B A A 5.5 Elastic Collisions 1 2 2 B 2 B A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? 20 10vA 5vB vA 2 .5vB 40 10v 5v 2 A 2 B 40 10(2 .5vB ) 5v 2 2 B 5.5 Elastic Collisions A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? vA 2 .5vB 40 10(2 .5vB ) 5v 2 2 B 40 10(.25v 2vB 4) 5v 2 B 40 2.5v 20vB 40 5v 2 B 2 B 2 B 0 7.5v 20vB 2 B 5.5 Elastic Collisions A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? 0 7.5v 20vB 2 B vB 2.67 ms m v 0 . 67 2020 10 vAvA 5(52s v.67 A 10 B ) Confirm 10(0.67 5(v2.67 40) 10 5)v 40.1 2 2 A 22 B 5.5 Elastic Collisions 5.7 Center of Mass The point where the system can be balanced in a uniform gravitational field Center of mass of Triangle Uniform objects center of mass is in the center Motion of CM 5.7 Center of Mass Center of mass is not always in the object Objects balance if supported at their center of mass 5.7 Center of Mass