Energy Energyis anything that can be con- verted into work; i.e., anything that can exert a force through a distance Energy 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.

1.Energy can be transferred from one object or system to another. Basic Properties of Energy

2.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.

Mechanical Energy Energy associated with motionEnergy associated with motion

Kinetic Energy Kinetic Energy: Ability to do work by virtue of motion. (Mass with velocity) A speeding car or a space rocket Types of Mechanical Energy KE = ½ mass x velocity 2 KE = ½ mv 2

Examples of Kinetic Energy What is the kinetic energy of a 5-g bullet traveling at 200 m/s? 5 g 200 m/s KE = 100 J How fast must a 700 kg car drive in order to have 78,750 J of kinetic energy?

Potential Energy Potential Energy: Ability to do work by virtue of position or condition. A stretched bow A suspended weight Types of Mechanical Energy Gravitational Potential Energy PE g = weight x height PE g = [mass X gravitational acceleration] X height PE g = mgh Elastic Potential Energy

What 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 2.7x10 10 Joules of gravitational potential energy. What is the mass of this airplane? Examples of Potential Energy PE = mgh = (50 kg)(9.8 m/s 2 )(480 m) PE = 235,200 J PE = mgh 2.7x10 10 J = (m)(9.8 m/s 2 )(11,000 m) m = 250,464 kg

Heat Energy Energy from the internal motion of particles of matterEnergy from the internal motion of particles of matter The hotter something is, the faster its molecules are moving around and/or vibrating, i.e. the more energy the molecules have.

Chemical Energy The energy from bonds between atoms or ionsThe energy from bonds between atoms or ions

Electromagnetic Energy Energy of moving electric chargesEnergy of moving electric charges

Nuclear Energy Energy from the nucleus of the atomEnergy from the nucleus of the atom –Fusion is when two atoms combine The SunThe Sun –Fission is when the atom splits Nuclear power plantNuclear power plant Mass-Energy Equivalence: E=mc 2

16 Conservation of Energy Students will: a)Identify situations on which conservation of mechanical energy is valid. b)Recognize the forms that conserved energy can take. c)Solve problems using conservation of mechanical energy.

17 Mechanical Energy Mechanical 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.

18 THE PRINCIPLE OF CONSERVATION OF MECHANICAL ENERGY The Total Mechanical Energy (TME) of an object remains constant as the object moves, in the absence of friction.

19 Conservation of Energy All Potential Energy, no Kinetic Energy 1/2 Potential Energy, 1/2 Kinetic Energy 1/4 Potential Energy, 3/4 Kinetic Energy No Potential Energy, all Kinetic Energy 3/4 Potential Energy, 1/4 Kinetic Energy

20 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.

21 Ski Jumping (no friction)

22 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/s 30 m continued on next slide m = 4 kgv i = 17 m/sv f = ? g = 9.8 m/sh i = 30 mh f = 0 m

23 Example 1 continued:

24 Example 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 m At 6 m: TME = PE i + KE i = mgh i + ½ mv i 2 = (10 kg)(9.8 m/s)(6 m) + ½ (10 kg)(0 m/s) 2 = 588 J + 0 J = 588 J 2 m At 2 m: TME = PE f + KE f = mgh f + ½ mv f 2 = (10 kg)(9.8 m/s)(2 m) + ½ (10 kg)(v f ) 2 = 196 J + ½ (10 kg)(v f ) 2 Therefore: 588 J = 196 J + ½ (10 kg)(v f ) J – 196 J = ½ (10 kg)(v f ) J = ½ (10 kg)(v f ) 2 solve for v f = 8.9 m/s

25 Example 3: A Daredevil Motorcyclist A 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 m/s 70 m 55 m v f = ?

26 Example 3 continued

27 Example 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 m continued on next slide

28 Example 4 - continued answer

Example 5: Unknown Mass A skier starts from rest and slides down the frictionless slope as shown. What is the skier’s speed at the bottom? H=40 m L=250 m start finish continued on next slide m = unknownv i = 0 m/sv f = ? g = 9.8 m/sh i = 40 mh f = 0 m

30 Example 5: Unknown Mass - continued You can divide the mass out of the above equation.

Example 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.