Lecture8 - PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 8...

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PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 8
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Work for nonconstant force Spring force Potential Energy of Spring Power Last Lecture F = ! kx PE = 1 2 kx 2 P = " W " t = " KE " t P = Fv F x x
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Chapter 6 Momentum and Collisions
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Momentum Definition: Newton’s 2 nd Law: r p = m r v r F = m " r v " t r F = " r p " t "
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Conservation of Momentum True for isolated particles (no external forces) Proof: Recall F 12 =-F 21 , (Newton’s 3 rd Law) for isolated particles never changes! r F 12 + r F 21 = 0 " # r p 1 # t + # r p 2 # t = 0 " # r p 1 + # r p 2 = 0 r p 1 f + r p 2 f = r p 1 i + r p 2 i r p i "
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Momentum is a Vector quantity Both ! p x and ! p y are conserved p x = mv x p y = mv y
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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
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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
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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 wench which winds 0.5 m of rope onto the boat every second. a) What is Ted’s velocity just after the wench 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
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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.
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