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

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.

Conservation of Mechanical Energy The mechanical energy of an isolated and friction free system is conserved U 1 + K 1 = U 2 + K 2

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

Elastic Potential Energy The energy stored in a compressed or stretched spring is: U s = ½ kx 2 k is the spring constant x is the elongation or compression from equilibrium

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

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 37 0 above the horizontal. A second ball is fired at an angle of 90 0 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)1.85x10 4 m, 5.10x10 4 m, b) 1.00x10 7 J )

Problem 3- The pendulum (#9) A pendulum has a 2.00m long string and the bob makes an initial angle of 30 0 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 Ans: a)2.29m/s, b)1.98m/s

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= ( kx 2 ) -x 2mgsinθ