Energy and Momentum

# Energy and Momentum - Vector problem from homework 3 What...

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Vector problem from homework 3 What is the path that allows the boy to cross the river in the shortest time? the correct answer is J the fastest way for the boy to reach the other side is to row straight across the river (even though the river will push him downstream) For which rowing orientation will the boy land on the opposite bank, directly across from his starting position the correct answer is A he has a velocity component opposite the river velocity that exactly compensates for the river trying to take him downstream

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Vector problem from homework 3 The time to row across for A is less than the time for D there is a larger component of horizontal velocity The distance traveled in crossing for C is greater than that for F the sum of the two vectors is larger The time to row across for K is greater than that for H again, there is a smaller component of horizontal velocity The time to row across for D is equal to that for K horizontal components are the same For an observer on shore,the speed of the boat for D is less than that for A vector sum is smaller
Bouncing ball p p Consider a ball bouncing on the floor in a perfectly elastic collision The magnitude of the momentum remains the same but the direction is 180 degrees opposite The change of momentum of the ball has a magnitude of 2|p| If it were a ball of clay (no bounce), the change of momentum of the ball is |p| If the momentum of the ball changes, is momentum not conserved? No, the momentum of the Earth has changed

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Water wheel The water wheels used in the California gold rush were not very effective A man named Lester Pelton realized that the impulse (momentum transfer) would be twice as great if he could get the water to “bounce” off the water wheel He probably earned more money from this invention than any of the miners earned from their gold strikes
Back to conservation laws A conservation law specifies that certain quantities in a system remain precisely constant, regardless of what changes may occur within the system Momentum is unchanged, i.e. is conserved Energy is also conserved as is angular momentum electric charge some subatomic properties that we’ll study later in the course

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Momentum We were talking about collisions and momentum conservation In the last lecture, we discussed elastic collisions To the right are two examples of inelastic collisions In both cases momentum is conserved the two trucks have the same total momentum after the collision as before We’ve learned that F= Δ p/ Δ t; if there are no external forces, there can be no change in the momentum of the system P initial = P final Suppose truck A has a mass of 1000 kg and truck B has a mass of 2000 kg and truck A is travelling at a speed of 30 m/s
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## This note was uploaded on 10/17/2011 for the course ECON 101 taught by Professor Thompson during the Spring '11 term at Michigan State University.

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Energy and Momentum - Vector problem from homework 3 What...

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