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## Kinetic and Potential Energy

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**Kinetic and Potential Energy**Physics Ms. Li**Kinetic Energy**• The energy of motion • The net work done on an object is equal to the change in kinetic energy of an object. • Work = ΔKE • Fd = mad= m(1/2(vf^2-vi^2)=1/2mvf^2-1/2mvi^2= KEf - KEi • Kinetic Energy • KE = ½mv2**This equation reveals that the kinetic energy of an object**is directly proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine.**Energy is scalar**• Kinetic energy is a scalar quantity; it does not have a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is completely described by magnitude alone.**Check Your Understanding**• 1. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s. • 2. If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy?**Check Your Understanding**• 1. KE = 0.5*m*v2 KE = (0.5) * (625 kg) * (18.3 m/s)2 • KE = 1.05 x105 Joules • 2. If the speed is doubled, then the KE is quadrupled. Thus, KE = 4 * (1.04653 x 105 J) = 4.19 x 105 Joules. or • KE = 0.5*m*v2 • KE = 0.5*625 kg*(36.6 m/s)2 • KE = 4.19 x 105 Joules**Examples**• 3.Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed? • 4. A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr.**Answers**• 3.KE = 0.5*m*v2 12 000 J = (0.5) * (40 kg) * v2 • 300 J = (0.5) * v2 • 600 J = v2 • v = 24.5 m/s • 4. KE = 80 000 J • The KE is directly related to the square of the speed. If the speed is reduced by a factor of 2 (as in from 60 mi/hr to 30 mi/hr) then the KE will be reduced by a factor of 4. Thus, the new KE is (320 000 J)/4 or 80 000 J.**How much work is required to accelerate a 1000 kg car from**20 m/s to 30 m/s? Example**5.A car traveling 60 km/hr can brake to a stop within a**distance of 20 m. If the car is going twice as fast, 120 km/h, what is its stopping distance? Example**What is Potential Energy?**• Stored energy. • Can be used later to do work • Depends on: • Position of object (ex. Height) • Configuration of object(ex. Stretched spring)**Examples of PE.**• Wound up clock spring. • A book about to fall off a table • Gasoline • Fuel**Gravitational PE**• Depends on height • Depends on mass • Depends on acceleration due to gravity • PEgrav= mgh**Work and PE**• When work is done on an object often the PE of an object changes. • If an object is lifted upward the PEgrav increases Hmm… that guy has a lot of PE!**Knowing that the potential energy at the top of the tall**platform is 50 J, what is the potential energy at the other positions shown on the stair steps and the incline?**Elastic PE**• Often when a spring is compressed it gains potential energy. • The formula for the force of a spring is F = -kx F = force(N) k = spring constant(N/m) x = displacement of spring (m)**Elastic PE**• When a spring is stretched or compressed there must be work done on the spring. • This work done gives the spring PE • Equation: PEelastic= ½kx2**A 1000 kg roller coaster moves from point A to point B and**then to point c. What is the change in PE as the car moves form B to C? Example B 10m A 15 m C**Mechanical Energy**• The total amount of potential and kinetic energy an object has. • If all the forces acting on an object are conservative then the total mechanical energy of the system can be given as: E = KE + PE + Q E = ½mv2+ PE +Q**Conservation of Energy**• The total mechanical energy of a system neither increases nor decreases in any process. It stays constant. This is true only if only conservative forces are acting in the system. • In other words : If an object falls all of its potential energy turns into kinetic energy by the time it reaches zero height.**Problem solving**• Remember that an objects PE changes into KE as it loses height. • For example, a ball rolls down a frictionless incline plane of height H. It then rolls up another frictionless incline plane of height 2H. • The height that the ball reaches must be only halfway up the second ramp. (H)**Examples**• Estimate the kinetic energy and the velocity required for a 70 kg pole vaulter to pass over a bar 5.0 m high. Assume the pole vaulter’s center of mass is initially 0.90 m off the ground and reaches its maximum height at the level of the bar itself. On board