Chapter9

Chapter9 - Chapter 9 Demos...

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PHYS276, S09 Chapter 6 1 Chapter 9 Demos: http://www.physics.umd.edu/deptinfo/facilities/lecdem/lecdem.htm B1-04: center-of-mass – brass barbell C1-01: center of mass motion – barbell C5-13: water rocket C7-11: collision of balls equal mass C7-23: medicine ball and skateboard Thanks to Prof LaPorta and “Peer Instruction” by Eric Mazur

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Conservations Laws PHYS276, S09 Chapter 6 2 We saw, in the last chapters, that conservation of energy was a very powerful, elegant method for solving simple kinematic problems. It turns out that conservation laws are related to symmetries. For every symmetry of nature, there is an associated conservation law. Conservation of energy is related to the fact that the laws of physics do not change with time. This chapter we will learn a new quantity, momentum, that is related to the fact that the laws of physics are the same everywhere in the universe. (translation symmetry) Conservation of momentum is useful for a wide variety of problems. We will find it especially useful for collision problems.
momentum PHYS276, S09 Chapter 6 3 Start with Newton’s third law: F 1 2 = F 2 1 m 1 a 1 + m 2 a 2 = 0 m 1 d v 1 dt + m 2 d v 2 dt = 0 d dt ( m 1 v 1 + m 2 v 2 ) = 0 m i v i = constant Note that this is a vector equation. Thus, the 3 components are separately conserved!

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momentum PHYS276, S09 Chapter 6 4 p = m v momentum is a vector • units are kg m /s • for a closed system (no external forces), momentum is conserved Ask yourself: • how is momentum different from kinetic energy? • how is momentum different from velocity? For a closed (isolated) system (no external forces), momentum is conserved. • is useful in more situations that conservation of energy • gives vector information
Conservation of momentum PHYS276, S09 Chapter 6 5 C7-23: medicine ball and skateboard A person weighing 60 kg is standing on a massless skateboard that rests on a frictionless surface holding a ball that weights 5 kg. She throws it at 10 m/s. What happens to her? initially, the momentum of woman and of ball=0 final momentum of ball = (5kg)(10m/s)=50kgm/s final momentum of woman = 60v 60v=50 kg m/s v=0.8 m/s

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Is energy conserved? 1. Yes 2. No Can you use conservation of energy to solve this problem? Why?
Test yourself PHYS276, S09 Chapter 6 7 Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown in the figure, is the cart put in motion? 1)yes, it moves to the right 2)Yes, it moves to the left 3)No, it remains in place

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Test yourself PHYS276, S09 Chapter 6 8 Suppose the entire population of the world gathers in one spot and, at the sounding of a prearranged signal, everyone jumps up. Just as the people leave the ground, does the earth gain momentum in the opposite direction? 1)Yes
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Chapter9 - Chapter 9 Demos...

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