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

-PotentialEnergy -Conservation of Mechanical Energy in an isolated system, without friction. AP Physics C Mrs. Coyle. Gravitational Potential Energy, Δ U g =mgh. h=height Unit: Joule Compared to a Reference (Base) level. When solving problems, be sure to select the reference level.

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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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