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Kinetic and Potential Energy Notes Chapter 5-2 Mechanical Kinetic Energy • Amount of energy an object has based on motion • Depends on the mass of the object and its speed • Kinetic Energy = ½ mass x velocity2 – KE = ½ mv2 • Units of Energy– (kg) (m/s)2 or kg m2 / s2 – Same as unit for work—Joules (J) • A 1400 kg car moving at a velocity of 18 m/s has what amount of Kinetic Energy? • How fast would a basketball with a mass of 2.3 kg have to go to have the same amount of kinetic energy as the above car? Work – Kinetic Energy Theorem • The amount of work done on an object can be translated into movement of the object • Work can be related to the change in the kinetic energy of the object – Called the Work-Kinetic Energy Theorem – Work = ∆ Kinetic Energy • W = ∆ KE Potential energy is stored energy --the energy is not being used now but could be used in the future --2 types: gravitational potential energy (PEg) elastic potential energy (PEe) Gravitational potential energy • the energy an object has based on position – depends on its mass, gravity, and its height above a reference point – gravity is trying to pull the object back down to the earth • Ex: apple on a tree, skier atop a hill, rock on cliff, etc. Gravitational potential energy formula Potential energy = mass x gravity x height PEg = mgh (F x d where F = mg and d = h) --units of Joules (kg x m/s2 x m) – Height is measured from a reference point • Usually the ground or the surface beneath the object • Can lead to a negative height – Ex. An object under water or below ground, any object below the reference point Sample problems • How much potential energy does a 55 g apple have hanging 3.5 meters high in a tree? • A 55 kg skateboarder is at the top of a ramp with a slope of 35 degrees. The ramp is 5.5 m long. How much potential energy does the person have? Elastic Potential Energy --the amount of energy in a stretched or compressed object --a stretched rubber band, a stretched spring, a compressed golf ball http://www.youtube.com/watch?v=2Y57pw_iWl k • the energy comes from the molecules wanting to return to their “normal” state – in stretching or compressing, the molecules get pushed closer to or pulled further from their neighboring molecules. – the energy comes from the attraction or repulsion of the molecules to return to their “relaxed” position • amount of energy is based on the strength of the spring or stretched object and the distance it is stretched • the spring constant (k) measures the strength of the spring or elastic object – the stronger the spring, the higher the k value – the farther the spring or elastic object is stretched, the greater strain on the moleculesthe more potential energy Elastic potential energy formula • potential energy = ½ x spring constant (k) x distance from relaxed state2 PEe = ½ k x2 --the spring constant has units of (N/m) so the units become (N/m) x m2 which reduces to N x m or Joules (J) Sample elastic potential problems • A person jumping on a pogo stick compresses a spring with a spring constant of 9800 N/m a distance of 15 cm. How much energy is stored in the spring? • A slingshot has a normal length of 26.0 cm. A person puts a marble in it and pulls it back to a length of 54.5 cm. The spring constant is 350 N/m. Find the energy of the rubber band.