Work energy

1. Work & energy Physics

2. What is Energy?? The ability to do work If an object has Energy, then it is able to move or transform things What is work? Work occurs when a force makes an object move Work is a transfer of energy When you do work on an object, you transfer energy from you to that object This implies that W =?E or the amount of work done on an object is equal to the gain or loss of E for that object

3. Work � Energy Theorem Work done is equal to the change of Energy of that object W=?E So, however much Energy an object gains or loses is equal to the amount of work done by/on it Work is a transfer of Energy from one object to another

4. Doin Work� When something is sped up or slowed down When something�s height above the ground is increased When a force makes an object move� W = Fd W � Work (J) F � Force (N) d - displacement (m)

5. Units for Work/Energy Unit of work (energy) is the N�m, or Joule (J) What else can energy be measured in? One Joule of energy is equal to 0.239 calories, or 0.000239 Calories (food) What does it mean to say a piece of food has 1oo calories?? Winter 2006 5

6. Dad applies force of 50 N of horizontal force, how much work is done? W = Fd Or in this case only the horizontal force is doing work so it becomes W = (F) d So W = (50)10 = 500 J If there is no friction, this means that the sled gained 500 J of KE

7. Work done vertically� Must be treated differently since gravity acts vertically Gravity can do work You can do work against gravity Since W = Fd to lift something you must apply a force equal to the weight of the object so in this case F = (mg) and �d� is equal to the increased or decreased height of the object

8. Work Examples How much work does it take to lift a 30 kg suitcase onto the table, 1 meter high? W = ?E = ?PE = PEf � PEi PEi = 0 So Work = PEf and PEf = mgh Sooo�. Work= mgh = (30 kg)(9.8 m/s2)(1 m) = 294 J Pushing a crate 10 m across a floor with a force of 250 N requires 2,500 J of work Gravity does 20 J of work on a 1 kg (10 N) book that it has pulled off a 2 meter shelf

9. Stairs vs. Ramp vs. direct lift  Raising which of these blocks requires the most work?? All the same, since they are all getting moved up to the same height they require the same amount of work done b/c they all gained the same amount of PE Which requires the least force? The ramp, because W = Fd since it has a longer distance to travel, the force is reduces. The other two since you are lifting it straight upwards require that you lift with a force equal to the object weight In this manner, a ramp can be very useful�.. Even though same work�.. Reduces force

10. In general Work is a scalar quantity, but are derived using F and d, two vector quantities, so Work still can be negative If force is in same direction as displacement then work is positive If force and displacement are in opposite directions, then amount of work is negative Examples Friction slowing down an object (-) Lifting a book unto a shelf (+) Lowering an object onto the ground (-) Pushing a cart along the ground (+) Football player tackles another play in a head on collision (-)

11. Many types of Energy Electrical Chemical Thermal Solar Mechanical Sound Nuclear

12. Mechanical Energy Gravitational Potential Energy An object is able to do work by virtue of its position above the Earth Stored Energy as a result of an objects position PEg = mgh h ? always measured from some reference level, usually ground Kinetic Energy An object is able to do work by virtue of its motion Energy of Motion KE = � mv2 Elastic Potential Energy Will be discussed later

13. Gravitational Potential Energy The energy an object has because of its height above the Earth is equal to the amount of work done by raising it This is in agreement with both W = ?E By lifting up something to a certain height you are increasing its PE, this increase is equal to the amt of work done And W = Fd F is equal to �mg� and the �d� is the same as the �h� So W = Fd = PE = mgh

14. Kinetic Energy The kinetic energy for a mass in motion is K.E. = �mv2 Example: 1 kg at 10 m/s has 50 J of kinetic energy Ball dropped from rest at a height h (P.E. = mgh) hits the ground with speed v. After ball falls, no PE left, all energy is now KE. Expect mgh =�mv2 In this case all of the PE converted into KE. So energy was conserved. 14

15. Conservation of Energy Energy can never be created nor destroyed Energy is never lost, only transferred This holds true for all forms of energy In any closed system the total amount of energy remains constant

16. Conservation of Mechanical Energy All mechanical energy must be conserved in any closed system In other words, the sum of all forms of mechanical energy stays constant MEi = Mef Or PEi + KEi = PEf + KEf

18. Elliptical Orbits When faster?? When Slower?? Why?? Just like falling objects, when you lose ht. you lose PE and gain KE So when close to sun we have converted most PE to KE and when we are far away vice versa

19. Power The rate at which work is done Units ? Watts (W) ? 1 W = 1 J/s P = W/ t OR since W = Fd we can say P = (Fd)/t which since v = (d/t) we can say P= Fv is an alternative form of the power equation, and can be used to express instantaneous power when velocity is not constant

20. Elastic Potential Energy PEE = � kx2 k = spring constant in N/m x = amount of compression or stretch in an elastic object from its equilibrium position This is the third type of mechanical energy PEE can also be transferred into PEG and KE and Cons. Of Mech. E also applies to conversions between this and the other types of ME