Lab 125 - y o is the distance the spring is stretched when...

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Lab 125 – Conservation of Energy Using a Spring – Mass System 10/27/06 Group 1: Russell Adams Pawel Bokota Vahid Hamidullah Physics 111A TA: Ke Su ( [email protected] ) 1. - Objective To verify the conservation of mechanical energy in an oscillating mass-spring system. 2. – Theory Derivation of the mechanical energy equation of a vertical oscillating spring: The total mechanical energy ME of the spring mass system is: 1. ME = ½(m)v 2 + ½(k)(y-y 0 ) 2 + mgy In this equation, the first term is kinetic energy (KE), the second term is the potential energy of the spring (PE), and the last term is the gravitational potential energy (PE g ). Where m is the mass of weight in kg, k is the spring constant in N/m, y is measured from the equilibrium position (upward positive),
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Unformatted text preview: y o is the distance the spring is stretched when it is in the equilibrium position (with mass m hanged). If the spring has a mass of m hanging on it, the elongation, y o = mg/k. (Rewriting equation (1) substituting: y o = mg/k ): 2. ME = ½(m)v 2 + ½(k)(mg/k – y) 2 + mgy = ½(m)v 2 = ½(m 2 )(g 2 )/k – mgy + ½(k)y 2 + mgy When we combine the two potential energy terms: 3. ME = ½(m)v 2 + ½(k)y 2 + (m 2 )(g 2 )/2k Since the last term on the right hand side is a constant, the sum of the first two terms on the right hand side must be a constant for mechanical energy to be conserved. 3. - Procedure The motion detector was connected to the ULI interface so that the spring constant could be measured....
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