Work & EnergyIn the past… v, a, x, t How things move, Kinematics F, a, m What makes them move, DynamicsNow we will look at WHY they move!!! Energy!Energy The ability to do work.
The theme of this unit is: Energy is Energy is Energy Color Code for this power point:• Energy words will appear in red.• Forces will appear in yellow.• Distances will appear in green.
Work = Force x Distance W=FxdIn units this means1 Joule = 1 Newton x 1 Meter Joule (J) is pronounced (jewel) and is the unit for Work (W) of any kind. W=FxdNewton (N) is the unit for Force (F) and W=FxdMeter is the unit for distance.
W=FxdFor Work (W) to take place on any object 1. There must be a force (F) 2. The object must travel a distance (d).• Anything that puts a force on an object displacing it will cause work.
Which of the following do work on the box? gravity No. Doesn’t move up or down normal force No. Doesn’t move up or down you pulling it Yes, but only the x direction. friction Yes, it opposes the motion.Positive energy is + if it is going into the object/systemNegative energy is – if it is coming out of the object/system
Example Problem:How much work will the road do on 18,000 N car when its brakes are applied, if the car skids 10 m? W=F xd W = 18000 N x 10 m W = 180,000 JWhich force is at work? Friction because it is opposing motion.
Remember the theme of this power point?Energy is Energy is Energy
What is that supposed to mean? Well, Energy is the ability to do workThe next slides will tie all energies together.
Law of It can only change form.Conservatio There are many forms of energy.n of Energy We will study four types. Energy 1.Workcannot be 2.Gravitational Potential Energycreated or 3.Kinetic Energydestroyed 4.Elastic Potential Energy Work: must be a force and distance W = F x d Gravitational Potential Energy: Energy due to position. Must be a height off the ground, gravity, and mass. GPE = m x g x h Kinetic Energy: Energy due to motion. Must have velocity and mass. KE = ½ mv2
The fourth type is called Elastic Potential Energy because it is energy due to springs or rubber bands.We will focus on springs for this lesson.So SPE means Spring Potential Energy.SPE requires obviously a spring and how strong it is. This is represented by little letter k in a formula.SPE also requires a measure of how far a spring is stretched or how far it is pushed together. SPE = (1/2) k x2
Conservation of EnergyNow that you know four types of energy andthe theme is Energy is Energy is Energy That meansWork = KE= GPE = SPEF x d = ½(mv2 ) = m x g x h =(1/2) kx2EACH TIME YOU CALCULATE ONE THE ANSWER FOR THE OTHERS IS THESAME FOR ONE SYSTEM.
Example:A 600 kg roller coaster car is lifted to the top of thefirst hill, 55 m above the ground. How muchPotential Energy is this?Use mass x gravity x height GPE = 600 x 9.8 x 55 GPE = 323400 JHow much Kinetic Energy does it have as it falls?323400 J.How much work did it take to lift it?323400 J. The answer is always the same.
Energy is Energy is Energy• No matter which one you are asked to calculate the other energies will have the same answer in a system.• This means only calculate the answer one time and use the answer for all four energies.
• Carefully read over the next slide. This will illustrate the point about always using the same answer for calculating energies.• Remember: Energy cannot be created or destroyed, it can only change form.
Gravitational Potential Kinetic EnergyEnergy energy due to motion energy due to position KE = ½ mv 2PE = mgh Ex. How much KE does an 1800Ex. You lift a 1.2 kg book from kg car going 25 mph (11.2 m/s)the first floor to your social have?studies class on the 2nd floor 5m up. How much potential KE = ½ mv2energy does the book have? = ½(1800)(11.2)2 = 113 000 JPE =mgh = (1.2) (9.8) (5) How much work would friction = 58.8 J need to do to stop it? W = KE = -113 000 JHow much work did you do? The answer is the same because of conservation ofConservation!!! energy. It’s the same = 58.8 J W = PE answer because of conservation.
Sample ProblemA disgruntled physics student dropsher 1.7 kg book off a 4 story building(12 m), What is the potential energy?What is the Kinetic Energy? What wasthe work done to lift it?h = 12 mm = 1.7 kgPE = m x g x hPE = 1.7 x 9.8 x 12PE = 199.92 JKE = 199.92 J and W = 199.92 J
Describe the energy transfer in the following Different Scenarios• Dropping an object off a building• Throwing an object off a building• Car being slowed down by friction• You throwing a ball• A bullet shot; then embedded in a tree• You lifting your backpack up to math
Work Energy Theorem W = Change in KE W = Change in PE W = Change in SPEIn order to change any type of energy, work must be done.
Work Energy Theorem practice• A 2.5 kg apple hangs from a tree 5 meters up. It falls to the ground. What is the potential energy of the apple in the tree?• What is the final velocity of the apple just before it hits the ground?• PE = m x g x h• 2.5 x 9.8 x 5 Ans. 122.5 J• KE = ½ mv2• 122.5 J = ½ x 2.5 x v2 122.5 = 1.25 x v2• 122.5/1.25 = v2• 98 = v2 So take the square root to get v 9.9 m/s = v