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-PotentialEnergy -Conservation of Mechanical Energy in an isolated system, without friction.

Learn about potential energy conservation in isolated systems without friction in AP Physics. Solve problems involving gravitational potential energy, elastic potential energy, and more. Includes detailed solutions for projectile motion, pendulum motion, and spring on inclined plane scenarios.

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-PotentialEnergy -Conservation of Mechanical Energy in an isolated system, without friction.

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  1. -PotentialEnergy-Conservation of Mechanical Energy in an isolated system, without friction. AP Physics CMrs. Coyle

  2. Gravitational Potential Energy, ΔU g=mgh • h=height • Unit: Joule • Compared to a Reference (Base) level. • When solving problems, be sure to select the reference level.

  3. Conservation of Mechanical Energy The mechanical energy of an isolated and friction free system is conserved U1 + K1 = U2 + K2

  4. Note In an isolated system there are no energy transfers across the boundaries.

  5. Elastic Potential Energy • The energy stored in a compressed or stretched spring is: Us = ½ kx2 • k is the spring constant • x is the elongation or compression from equilibrium

  6. Problem 1- The loop-the-loop (#5) A bead slides with out friction around a loop-the-loop. The bead is released from a height h=3.5R. a) What is the speed at the top of the loop? b) How large is the normal force on it if its mass is 5.00g? Ans: a) v=(3gR) ½, b) 0.098N

  7. Problem 2- Projectile(#17) A 20.0 kg cannon ball is fired from a cannon with a muzzle speed of 1,000m/s at an angle of 370 above the horizontal. A second ball is fired at an angle of 900 with the same speed. Find: a) the maximum height reached by each ball. b) the total mechanical energy at the maximum height for each ball. Set the reference point to be at the cannon. (Ans: a)1.85x104m, 5.10x104m, b) 1.00x107 J )

  8. Problem 3- The pendulum (#9) A pendulum has a 2.00m long string and the bob makes an initial angle of 300 with the vertical when the bob is released (ignore air resistance). Calculate the speed of the particle: a) at the lowest point of the swing and b) when the angle is 150. Ans: a)2.29m/s, b)1.98m/s

  9. Problem 4- Spring on an inclined plane (#10) • An object of mass m starts from rest and slides a distance d down a frictionless incline of angle θ. When sliding, it compresses a spring, of force constant k, a distance x at which point is it momentarily at rest. Find the initial separation d between the object and the spring. • Ans: d= ( kx2 ) -x 2mgsinθ

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