# energy - Mechanics and Modern Physics Dr. Bernd Stelzer...

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Dr. Bernd Stelzer Mechanics and Modern Physics PHYS 120 SFU Fall 2010 Dr. Bernd Stelzer

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Energy 10/20/10 This pole vaulter can lift herself nearly 6 m (20 ft) off the ground… …transforming the kinetic energy of her run into gravitational potential energy Goal: Introduce the ideas of kinetic and potential energy and conservation of energy. PHYS120 2 Bernd Stelzer
Energy in Free Fall Motion 10/20/10 F net = mg = ma y = m dv y dt dv y dt = dv y dy dy dt = v y dv y dy mv y dv y dy = mg mv y dv y = mgdy mv y dv y v iy v fy = mgdy y i y f 1 2 mv y 2 v iy v fy = 1 2 mv fy 2 1 2 mv iy 2 = mgy y i y f = mgy f + mgy i 1 2 mv fy 2 + mgy f = 1 2 mv iy 2 + mgy i K f + U f = K i + U i Newton’s 2 nd Law: Using chain rule: Conservation of mechanical energy PHYS120 3 Bernd Stelzer

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Forms of Energy 10/20/10 • Energy is a scalar quantity (not a vector) • Kinetic energy depends on an object’s speed (not velocity) • Energy can be transformed from one form to another. SI unit of Energy: [kg . m 2 /s 2 ] = 1Joule = 1J PHYS120 4 Bernd Stelzer
Swinging Pendulum 10/20/10 PHYS120 5 Bernd Stelzer GPE = mgy KE = 1 2 mv 2

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Energy Bar Chart for a thrown Ball 10/20/10 PHYS120 6 Bernd Stelzer
Example: 10/20/10 1 2 mv fy 2 + mgy f = 1 2 mv iy 2 + mgy i You throw a ball vertically up with initial velocity v iy . How high will the ball fly up before turning around? 0 0 mgy f = 1 2 mv iy 2 y f = v iy 2 2 g v fy 2 v iy 2 = 2( g )( y f y i ) y f = v iy 2 2 g 0 Note: How would we have solved this using kinematic equations of motion? E.g. Using (K3) with a y =-g y 0 PHYS120 7 Bernd Stelzer

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Question: 10/20/10 Q: A small child slides down the four frictionless slides A–D. Each has the same height. Rank in order, from largest to smallest, her speeds v A to v D at the bottom. A. v C > v A = v B > v D B. v C > v B > v A > v D C. v D > v A > v B > v C D. v A = v B = v C = v D E. v D > v A = v B > v C PHYS120 8 Bernd Stelzer
Question: 10/20/10 Q: A small child slides down the four frictionless slides A–D. Each has the same height. Rank in order, from largest to smallest, her speeds v A to v D at the bottom. A. v C > v A = v B > v D B. v C > v B > v A > v D C. v D > v A > v B > v C D. v A = v B = v C = v D E. v D > v A = v B > v C Conservation of mechanical energy holds for a particle moving along any frictionless surface, independent of path. 1 2 mv fy 2 + mgy f = 1 2 mv iy 2 + mgy i PHYS120 9 Bernd Stelzer

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Question: 10/20/10 Q: A small child slides down the four frictionless slides A–D. Each has the same height. Rank in order, from largest to smallest, her speeds v A to v D at the bottom. A. v C > v A = v B > v D B. v C > v B > v A > v D C. v D > v A > v B > v C D. v A = v B = v C = v D E. v D > v A = v B > v C PHYS120 10 Bernd Stelzer v fy 2 v iy 2 = 2 (a x )(y f y i ) v fy 2 = 2 (g sin θ )(L) v fy 2 = 2 )( h sin ) 1 2 v fy 2 = gh 1 2 mv fy 2 = mgh 0 a x = g sin В Example: Along the slope:
Zero Potential Energy 10/20/10 PHYS120 11 Bernd Stelzer

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