Energy Physics 2013 Energy Intro

Isaac Newton almost singe-handedly invented the science of mechanics, but there is one concept he missed! Energy comes in many different forms and has many definitions. But the most basic definition of energy comes in terms of work. Energy is the capacity to do work!

Energy The release of energy does work – and doing work on something adds energy to it. Energy and work are EQUIVALENT CONCEPTS and we can say that  same units! (J)

Forms of Energy Copywrited by Holt, Rinehart, & Winston Chemical Electrical Nuclear Thermal

Show Me the Money Liquid Asset: Cash Saved Asset: Stocks Income Expenses Transformations within system System Transfers into and out of system

The Basic Energy Model

Kinetic Energy If you throw a ball. You do work getting the ball moving: You exert a force over a distance. The ball has acquired some energy, the energy of motion, or Kinetic Energy (E K ) A “simple” mathematical derivation shows that E K = ½ mv 2 Where m = mass (kg) and v = velocity in (m/s)

Kinetic Energy Derivation Assume: V o = 0 Therefore, E K = W = Fd = mad F = ma v avg = v avg Rearranging, Substituting, Kinetic Energy = ½ mass x speed 2 Joules = kg (m/s) 2 E K = ½ mv 2

Kinetic Energy Kinetic Energy  Energy of Motion Example Problem: How much kinetic energy does a.25 kg baseball that is thrown with a velocity of 9.3 m/s have? m =.25 kg v = 9.3 m/s E K = 1/2mv 2 =10.8 J

Work – Energy Theorem the net work done on an object equals its change in kinetic energy. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

Example A space probe of mass m = 5.00 x 10 4 kg is traveling at a speed of v o = 1.10 x 10 4 m/s through deep space. No forces act on the probe except that generated by its own engine. The engine exerts a constant external force of magnitude 4.00 x 10 5 N, directed parallel to the displacement of magnitude 2.50 x 10 6 m. Determine the final speed of the probe. m = 5.00 x 10 4 kg v o = 1.10 x 10 4 m/s F = 4.00 x 10 5 N d = 2.50 x 10 6 m v f = ? Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

Potential Energy Suppose you lift an object to a certain height. As you exert a force (the object’s weight) over the distance, you do work. The object isn’t moving in the end, but energy has still has added because of where it is in the Earth’s gravitational field. This type of energy is called Potential Energy (energy of position) and is written E P or U where

Potential Energy E P is divided into categories according to its system: Mechanical –Gravitational –Elastic Chemical Electrical Nuclear Thermal

Gravitational PE Work is required to elevate objects against Earth’s gravitational field. The potential energy due to elevated positions is called gravitational PE. At A: the body possesses U g because the force of gravity acts on it. At B: the body possesses more U g than it did at A because work has been done lifting it. U g = E P = mgh

Copywrited by Holt, Rinehart, & Winston Gravitational PE Calculated relative to a reference point Path Independent Calculate the PE at points A-E Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

Consider a spring being extended by a steadily increasing force. When the force has a magnitude F, the extension is x. This relationship is known as Hooke’s Law F s =restoring force of a spring k = spring constant x= displacement of the spring Note: the negative sign indicates that the restoring force of a spring always points in a direction opposite to the displacement of the spring. Elastic Potential Energy F s =-kx Copywrited by Holt, Rinehart, & Winston

Elastic Potential Energy A graph of force against extension would be a straight line passing through the origin, as long as the elastic limit of the spring has not been exceeded (Hooke’s law). The slope of the graph is k, the elastic constant of the spring  F = kx

Elastic Potential Energy The work done increasing the length of the spring by x is given by: W = average force × extension The area under the curve or So, the elastic potential energy (U S ) stored in the spring is given by: W = ½ Fx = ½ kx² U S = ½ kx²

Potential Energy  Kinetic Energy Potential energy is “potential” because it can be gotten back as “real” kinetic energy. All you have to do is let the object fall! As the object falls faster and faster its potential energy is slowly converted to kinetic energy. At the bottom, just before impact, its potential energy is gone and its original potential energy has become entirely kinetic. U g0 =K Ef Mathematically, that is:

Example Problem A 15 kg ball falls from a roof 8.0 meters about the ground. What is its kinetic energy as it hits the ground? K/Um=15 kgh = 8.0 mg = 9.81 m/s 2 E Kf =U g0 =mgh E K = 1177 J ~1200 J Solving for speed  E kf =U g0 =½mv 2 v = m/s ~13 m/s

Clicker Understanding A child is on a playground swing, motionless at the highest point of his arc. As he swings back down to the lowest point of his motion, what energy transformation is taking place? A. B. C. D. E. A. B. C. D. E.

Clicker Understanding A skier is moving down a slope at a constant speed. What energy transformation is taking place? A. B. C. D. E. A. B. C. D. E.

Conservation of Energy The equality ½ mv 2 = mgh is an example of Conservation of Energy Energy can neither be created nor destroyed, but can only be converted from one form to another.

Conservation of Energy What happens to an object’s energy when it finally hits the floor and both its kinetic and potential energy are zero? Look at the impact itself. Some of the energy is converted into sound. Some goes into distorting the floor – and distorting the object for that matter. Some – really most – goes into heat. The object and the floor are both a little warmer after the collision. The impact jiggles their molecules – and heat is nothing both the kinetic energy of billions of molecules!

Conservation of Energy

The total mechanical energy (E = KE + PE) of an object remains constant as the object moves, provided that the net work done by external nonconservative forces is zero. Conservative Forces 1. The work it does on a moving object is independent of the path of the motion between the object's initial and final position. 2. The work it does moving an object around a closed path is zero 3. The work it does is stored in the form of energy that can be released at a later time. 4. Work done by a conservative force is the negative of the change in the potential energy Principle of Conservation of Mechanical Energy

Conservative Force Example: Gravity, Spring Force

Non-conservative Force Non-conservative Forces 1.Path dependent 2.Work done on a closed path is not zero. 3.Work done by a nonconservative force changes a system’s mechanical energy. 4.Work done by a nonconservative force equals the change in a system’s mechanical energy. Examples: Friction, Air resistance, tension, force exerted by muscles, force exerted by motor

Principle of Conservation of Mechanical Energy Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

Principle of Conservation of Mechanical Energy

Principle of Conservation of Mechanical Energy

Principle of Conservation of Mechanical Energy Conservation of Energy Elastic Potential Energy (Bungee) Real Bungee

Principle of Conservation of Mechanical Energy 1.Identify the forces (conservative and nonconservative) –Any nonconsevative force must do no work. 2.Choose the location where the U G is zero. 3.Set the final total E of the object equal to the initial total E. –The total E is the sum of the E K and U G. What is the speed of the bicyclist at the bottom of the hill assuming that she is coasting down the hill?

Principle of Conservation of Mechanical Energy 1.F weight  conservative 2.U G is zero at bottom of the hill. 3. What is the speed of the bicyclist at the bottom of the hill assuming that she is coasting down the hill? V f = 20.4 m/s

Work-Energy Theorem (Expanded) The net work done by all the external nonconservative forces equals the change in the object's kinetic energy plus the change in its gravitational potential energy. W nc =  E K +  U G W nc = (E Kf – E K0 ) + (U Gf – U G0 ) W nc = (1/2mv f 2 - 1/2mv 0 2 ) + (mgh f – mgh 0 )

Work-Energy Theorem

Work-Energy Theorem A hotwheels car sliding down a slope into a cup.

Work-Energy Theorem

Work-Energy Theorem Braking Problem

Braking Distance

Law of Conservation of Matter and Energy Energy cannot be created or destroyed; it may be transformed from one form to another, or transferred from one place to another, but the total amount of energy never changes. Matter and energy are interchangeable only when the total amount of matter is converted. c = 3 x 10 8 m/s (speed of light) E = mc 2