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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 = Δ KE Fd = mad= m(1/2(vf^2-vi^2)=1/2mvf^2-1/2mvi^2= KEf - KEi Kinetic Energy KE = ½mv 2.
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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