lecture notes-Chapter7-posted

lecture notes-Chapter7-posted - Chapter 7: Linear Momentum...

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1 Chapter 7: Linear Momentum Definition of Momentum Impulse Conservation of Momentum Center of Mass Motion of the Center of Mass Collisions (1d, 2d; elastic, inelastic)
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2 § 7.1 Momentum Why do need to define momentum? Consider two interacting bodies:
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3 The quantity (m v ) is called momentum ( p ). p = m v and is a vector. The unit of momentum is kg m/s; there is no derived unit for momentum.
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4 § 7.2 Impulse ) ( impus t = F p Definition of impulse: One can also define an average impulse when the force is variable. The change of momentum equals the impulse. ) ( net t m t = = F a v
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5 Example (text conceptual question 7.2): A force of 30 N is applied for 5 sec to each of two bodies of different masses. 30 N m 1 or m 2 Take m 1 <m 2 (a) Which mass has the greater momentum change? t = F p Since the same force is applied to each mass for the same interval, p is the same for both masses.
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6 (b) Which mass has the greatest velocity change? Example continued: m p v = Since both masses have the same p , the smaller mass (mass 1) will have the larger change in velocity. (c) Which mass has the greatest acceleration? t = v a Since a ∝∆ v the mass with the greater velocity change will have the greatest acceleration.
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7 Example (text problem 7.9): An object of mass 3.0 kg is allowed to fall from rest under the force of gravity for 3.4 seconds. What is the change in momentum? Ignore air resistance. Want p =m v . (downward) m/s kg 100 p m/sec 3 . 33 = = - = - = = v m t g v t a v
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8 Example (text problem 7.10): What average force is necessary to bring a 50.0-kg sled from rest to 3.0 m/s in a period of 20.0 seconds? Assume frictionless ice. ( 29 ( 29 N 5 . 7 s 0 . 20 m/s 0 . 3 kg 0 . 50 = = = = = av av av F t m t t v p F F p The force will be in the direction of motion.
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9 Question 2 An 18-wheeler and a Volkswagon Beetle are rolling along with the same momentum . If you exert the same force with the brakes to stop each one, which takes a longer time to bring to rest? A) 18-wheeler B) Volkswagon beetle C) same for both D) impossible to say
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10 § 7.3 Conservation of Momentum v 1i v 2i m 1 m 2 m 1 >m 2 m 1 m 2 A short time later the masses collide. What happens?
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11 During the interaction: N 1 w 1 F 21 N 2 w 2 F 12 x y 1 1 21 1 1 0 a m F F w N F x y = - = = - = 2 2 12 2 2 0 a m F F w N F x y = = = - = There is no net external force on either mass.
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The forces F 12 and F 21 are internal forces. This means that: ( 29 f f i i i f i f 2 1 2 1 2 2 1 1 2 1 p p p p p p p p p p + = + - - = - - = In other words, p i = p f . That is, momentum is conserved. This statement is valid during the interaction only.
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This note was uploaded on 12/23/2011 for the course PHY 2130 taught by Professor Rehse during the Fall '08 term at Wayne State University.

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lecture notes-Chapter7-posted - Chapter 7: Linear Momentum...

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