energy energyis anything that can be con- verted into work; i.e., anything that can exert a force...
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EnergyEnergy is anything that can be con-verted into work; i.e., anything that can exert a force through a distance.Energy is the ability to do work.
1Energy can be transferred from one object or system to another.Basic Properties of Energy
22.Energy comes in multiple forms.
3.Energy can be converted from any one of these forms into any other.
4.Energy is never created anew or destroyed - this is The Law of Conservation of Energy.
Basic Types of EnergyMechanical Energy
Energy associated with motion
7Kinetic EnergyKinetic Energy: Ability to do work by virtue of motion. (Mass with velocity)
A speeding car or a space rocketTypes of Mechanical Energy
KE = mass x velocity2KE = mv2
8Examples of Kinetic Energy
What is the kinetic energy of a 5-g bullet traveling at 200 m/s?5 g200 m/sKE = 100 J
How fast must a 700 kg car drive in order to have 78,750 J of kinetic energy?9Potential EnergyPotential Energy: Ability to do work by virtue of position or condition.
A stretched bowA suspended weight
Types of Mechanical EnergyGravitational Potential EnergyPEg = weight x heightPEg = [mass X gravitational acceleration] X heightPEg = mghElastic Potential Energy10What is the potential energy of a 50 kg person in a skyscraper if he is 480 m above the street below?
A typical 747 airplane flying at an altitude of 11 km has 2.7x1010 Joules of gravitational potential energy. What is the mass of this airplane? Examples of Potential Energy
PE = mgh = (50 kg)(9.8 m/s2)(480 m)PE = 235,200 JPE = mgh2.7x1010 J = (m)(9.8 m/s2)(11,000 m)m = 250,464 kg11Mechanical Energy and Conservation of EnergyHeat Energy
Energy from the internal motion of particles of matterThe hotter something is, the faster its molecules are moving around and/or vibrating, i.e. the more energy the molecules have.
12Chemical EnergyThe energy from bonds between atoms or ions
Energy of moving electric charges
14Nuclear EnergyEnergy from the nucleus of the atomFusion is when two atoms combineThe SunFission is when the atom splitsNuclear power plant
Mass-Energy Equivalence: E=mc2
1516Conservation of EnergyStudents will:Identify situations on which conservation of mechanical energy is valid.Recognize the forms that conserved energy can take.Solve problems using conservation of mechanical energy.1617Mechanical EnergyMechanical Energy is the sum of kinetic energy and all forms of potential energy in a system.In the absence of nonconservative resistive forces like friction and drag, mechanical energy is conserved.When we say that something is conserved, we mean that it remains constant.1718THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGYThe Total Mechanical Energy (TME) of an object remains constant as the object moves, in the absence of friction.
1819Conservation of Energy
All Potential Energy, no Kinetic Energy1/2 Potential Energy, 1/2 Kinetic Energy1/4 Potential Energy, 3/4 Kinetic EnergyNo Potential Energy, all Kinetic Energy3/4 Potential Energy, 1/4 Kinetic Energy1920
If friction and wind resistance are ignored, a bobsled run illustrates how kinetic energy can be converted to potential energy, while the total mechanical energy remains constant. 2021Ski Jumping (no friction)
Example 1: A person on top of a building throws a 4 kg ball upward with an initial velocity of 17 m/s from a height of 30 meters. If the ball rises and then falls all the way to the ground, what is its velocity just before it hits the ground?
17 m/s30 mcontinued on next slidem = 4 kgvi = 17 m/svf = ?g = 9.8 m/shi = 30 mhf = 0 m
Example 1 continued:2324Example 2: A 10 kg stone is dropped from a height of 6 meters above the ground. Find the Potential Energy, Kinetic Energy, and velocity of the stone when it is at a height of 2 meters.6 mAt 6 m:TME = PEi + KEi= mghi + mvi2 = (10 kg)(9.8 m/s)(6 m) + (10 kg)(0 m/s)2 = 588 J + 0 J = 588 J2 mAt 2 m:TME = PEf + KEf = mghf + mvf2 = (10 kg)(9.8 m/s)(2 m) + (10 kg)(vf)2 = 196 J + (10 kg)(vf)2 Therefore: 588 J = 196 J + (10 kg)(vf)2 588 J 196 J = (10 kg)(vf)2 392 J = (10 kg)(vf)2 solve for vf = 8.9 m/s2425Example 3: A Daredevil MotorcyclistA motorcyclist (300 kg including the bike) is trying to leap across the canyon by driving horizontally off a cliff with an initial speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.
38.0 m/s70 m70 m70 m55 m
vf = ?2526
Example 3 continued2627Example 4:Starting from rest, a child on a sled zooms down a frictionless slope from an initial height of 8.00 m. What is his speed at the bottom of the slope? Assume he and the sled have a total mass of 40.0 kg.
continued on next slide2728
Example 4 - continued
answer28Example 5: Unknown MassA skier starts from rest and slides down the frictionless slope as shown. What is the skiers speed at the bottom?H=40 mL=250 mstartfinish
continued on next slidem = unknownvi = 0 m/svf = ?g = 9.8 m/shi = 40 mhf = 0 m2930Example 5: Unknown Mass - continued
You can divide the mass out of the above equation.
30Example 6:A ball is dropped from a height of 5 meters above the ground. Using conservation of energy formulas, determine the speed of the ball just before it hits the ground.