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6 Momentum IVC_Fall 2008

# 6 Momentum IVC_Fall 2008 - Ming Dynasty 16th Century Woman...

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x cm = Σ m i x i / M Where M = Σ m i y cm = Σ m i x i / M + + + + + + = m m m x m x m x m x 3 2 1 3 3 2 2 1 1 cm + + + + + + = m m m y m y m y m y 3 2 1 3 3 2 2 1 1 cm Ming Dynasty 16 th Century Woman Standing Artist Tang Yin Definition of Center of Mass

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+ + + + + + = m m m r m r m r m r 3 2 1 3 3 2 2 1 1 cm Center of mass is a vector; its components add like vectors to make a vector r. Each r adds like vectors to make a total center of mass vector: i i i m r m = In statistical language, the center of mass is a mass- weighted average position of the particles. Ming Dynasty Blue and white porcelain with flower motif. 1426-1435
Momentum Momentum (mv), like all great principles in science, has a historical development. No one person can truly be credited with formulating the great principles of science. There was always someone else who opened the way for great minds. This was true for Newton as well as Einstein. m v M v m v m v m v

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The net force acting on a particle equals the time rate of change of momentum of the particle. Thus a rapid change of momentum requires a large net force. Newton’s second law can now be written in terms of the time rate of change of momentum (as Newton did. p = mv F a m t v m t v m t p = = = =
Momentum is a vector Momentum is a vector and is defined to be m v . Like all vectors it has a magnitude and components: p x = mv x ; p y = mv y ; p z = mv z At first momentum of red ball is mv = m0 = 0 As ball moves, mv is no longer zero. This implies momentum is changing with respect to time--hence a force is acting on the red ball. m v Note the m is a scalar while v is a vector—hence the product m v is simply scalar multiplication. t v m t p a m F = = =

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What is the Momentum of catching a ball? 0.50 kg ball moving at 4.0m/s 0.10 kg ball moving at 20 m/s
Both have the same momentum : p = mv = 2.0 kg m/s . However as we will see they have different kinetic energies . The slow ball has K = 4.0 J whereas the smaller fast ball has K = 20J . Thus your had must do 5 times more work to stop the small ball than the large slower ball.

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Mathematically, momentum is a vector whose magnitude is proportional to speed mv. Let us look at a new quantity called impulse, which we will show is directly related to the change in momentum of an object. Impulse is intimately tied to momentum
Question : Does the total momentum change differ if you catch the egg more slowly or is it the same?

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In bringing an egg to rest, the change in momentum is the same whether you use a large force during a short time interval or a small force during a long time interval. Of course, which method you choose makes a lot of difference in whether or not the egg breaks! A quantity called impulse may have been defined for you in lecture or in your textbook.
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