chapter6.key - Momentum Definition: ! ! p = mv ! ! ! !v !p...

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Chapter 6 Momentum and Collisions Momentum Defnition: Important because it is CONSERVED prooF: Since ± 12 =-± 21 , For isolated particles never changes! ! p = m ! v ! F = m ! ! v ! t = ! ! p ! t ! F ! t = ! ! p ! ! p 1 + ! ! p 2 = 0 ! p i ! Vector quantity Both ! p x and ! p y are conserved p x = mv x p y = mv y Example 6.1 An astronaut of mass 80 kg pushes away from a space station by throwing a 0.75- kg wrench which moves with a velocity of 24 m/s relative to the original frame of the astronaut. What is the astronaut’s recoil speed? 0.225 m/s Center of mass does not accelerate X cm ! m 1 x 1 + m 2 x 2 + m 3 x 3 + ... ( m 1 + m 2 + m 3 + ...) ! X cm = m 1 ! x 1 + m 2 ! x 2 + m 3 ! x 3 + ... ( m 1 + m 2 + m 3 + ...) = ! t " m 1 ( ! x 1 / ! t ) + m 2 ( ! x 2 / ! t ) + m 3 ( ! x 3 / ! t ) + ... ( m 1 + m 2 + m 3 + ...) = ! t " p 1 + p 2 + p 3 + ... ( m 1 + m 2 + m 3 + ...) = 0 if total P iszero Do the back-to-back demo
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Example 6.2 Ted and his ice-boat (combined mass = 240 kg) rest on the frictionless surface of a frozen lake. A heavy rope (mass of 80 kg and length of 100 m) is laid out in a line along the top of the lake. Initially, Ted and the rope are at rest. At time t=0, Ted turns on a winch which winds 0.5 m of rope onto the boat every second. a) What is Ted’s velocity just after the winch turns on? b) What is the velocity of the rope at the same time? c) What is the Ted’s speed just as the rope finishes? d) How far did the center-of-mass of Ted+boat+rope move e) How far did Ted move? f) How far did the center-of-mass of the rope move? 0.125 m/s -0.375 m/s 0 0 12.5 m -37.5 m Example 6.3 A 1967 Corvette of mass 1450 kg moving with a velocity of 100 mph (= 44.7 m/s) slides on a slick street and collides with a Hummer of mass 3250 kg which is parked on the side of the street. The two vehicles interlock and slide off together. What is the speed of the two vehicles immediately after they join? 13.8 m/s =30.9 mph Impulse Useful for sudden changes when not interested in force but only effects of force Impulse = F ! t = ! p Bunjee Jumper Demo Graphical Representation of Impulse For complicated force, " p is area under F vs. t curve F t Total Impulse " t F Impulse = F ! t = ! p Example 6.4 A pitcher throws a 0.145-kg baseball so that it crosses home plate horizontally with a speed of 40 m/s. It is hit straight back at the pitcher with a final speed of 50 m/s. a) What is the impulse delivered to
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chapter6.key - Momentum Definition: ! ! p = mv ! ! ! !v !p...

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