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Physics 1A, Section 2

This text discusses the principle of energy conservation in physics, highlighting its applications in both mechanical and non-mechanical systems. It explains that energy in a closed system is conserved, resulting in a constant sum of kinetic (K), potential (U), and heat energy. Mechanical energy may remain constant in ideal conditions (K + U = constant), illustrated by the equation ½ mv² + mgh. However, in real-world scenarios involving friction or inelastic collisions, mechanical energy is not conserved, leading to energy loss primarily as heat. Alternative methods, like work done by forces, help calculate energy in such cases.

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Physics 1A, Section 2

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  1. Physics 1A, Section 2 October 28, 2010

  2. Quiz Problem 49

  3. Quiz Problem 49 • Answer: • {[k3 + (k1-1 + k2-1)-1]-1 + k4-1]-1

  4. Energy Conservation • Energy is conserved: K + U + heat + … = constant • Sometimes, mechanical energy is conserved: • K + U = mechanical energy = constant • Example: ½ mv2 + mgh = constant • This often allows a quick solution of a difficult problem.

  5. Energy Conservation • Energy is conserved: K + U + heat + … = constant • Sometimes, mechanical energy is conserved: • K + U = mechanical energy = constant • Example: ½ mv2 + mgh = constant • This often allows a quick solution of a difficult problem. • However, in other cases, mechanical energy is not conserved, so K + U  constant: • friction: Energy is lost to heat. • inelastic collision: Energy is lost to heat. • This is the same thing as saying the force can’t be described by a potential energy; the force is a function of some variable other than position.

  6. Energy Conservation • Energy is conserved: K + U + heat + … = constant • Sometimes, mechanical energy is conserved: • K + U = mechanical energy = constant • Example: ½ mv2 + mgh = constant • This often allows a quick solution of a difficult problem. • However, in other cases, mechanical energy is not conserved, so K + U  constant: • friction: Energy is lost to heat. • inelastic collision: Energy is lost to heat. • This is the same thing as saying the force can’t be described by a potential energy; the force is a function of some variable other than position. • In some of those cases, one can resort to using the force to calculate the energy added to the system: energy input = W = ∫F•ds

  7. Quiz Problem 50

  8. Quiz Problem 50 • Answer: • v = sqrt(2gh) • F = -kx – mmg, to the right • W = -kxs2/2 – mmgxs • Wf = 2mmgxs • h’ = h – 2mxs • xs = [-mmg + sqrt(m2m2g2+2kmgh)]/k

  9. Monday, November 1: • something to do with potential energy

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