PHY183-Lecture21 - Physics for Scientists&Engineers 1 1 Physics for Scientists& Physics for Scientists& Engineers 1 Engineers 1 Spring

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Unformatted text preview: February 20, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 21 February 20, 2006 Physics for Scientists&Engineers 1 2 Energy Review Energy Review Conservation of Energy Kinetic Energy Gravitational Potential Energy Spring Potential Energy U g ( y ) = mgy + constant U s ( x ) = 1 2 kx 2 + constant K + U = K + U K = 1 2 mv February 20, 2006 Physics for Scientists&Engineers 1 2 Energy Review Energy Review Conservation of Energy Kinetic Energy Gravitational Potential Energy Spring Potential Energy U g ( y ) = mgy + constant U s ( x ) = 1 2 kx 2 + constant K + U = K + U K = 1 2 mv 2 February 20, 2006 Physics for Scientists&Engineers 1 3 Example: Defending the Castle Example: Defending the Castle Defend castle from attackers! Shoot rocks from catapult with launch speed of 14.2 m/s, from the courtyard over the castle walls onto the attackers in front of the castle, at elevation 7.2 m below courtyard. Question: What is speed with which your rocks hit the attackers? Answer: Hard way: find appropriate launch angle to clear wall; decompose initial velocity vector into components; solve for y-component of velocity as a function of time or altitude, following trajectory to impact; take square root of sum of the squares of the velocity components February 20, 2006 Physics for Scientists&Engineers 1 4 Example: Defending the Castle Example: Defending the Castle Answer: Much easier way: use energy conservation Insert numbers K + U = K + U 1 2 mv 2 + mgh = 1 2 mv 2 + mgh v = v 2 + 2 g ( h ! h ) v = (14.2 m/s) 2 + 2 ! (9.81 m/s 2 ) ! (7.2 m) = 18.5 m/s February 20, 2006 Physics for Scientists&Engineers 1 5 Quiz 21.1 Quiz 21.1 A 0.400-kg bead slides on a curved wire, starting from rest at point A in the figure below. If the wire is frictionless, find the speed of the bead at C ....
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This note was uploaded on 03/19/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture21 - Physics for Scientists&Engineers 1 1 Physics for Scientists& Physics for Scientists& Engineers 1 Engineers 1 Spring

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