Work & energy

1. Conceptual Physics Work & energy

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=ΔE • 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??

6. Work done horizontally…. • 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 – PEiPEi = 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 = ½ 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 h

14. Kinetic Energy • The kinetic energy for a mass in motion is K.E. = ½mv2 • 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 =½mv2 • In this case all of the PE converted into KE. So energy was conserved.

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 = ½ 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