1. WORK & POWER

2. Energy Review: What is energy?  The capacity to cause change  Stored within system(E g, E el, E k, E int )  Added to or removed from the system through “working”(W)

3. Basic Energy Model: Expanded E total = E k + E el + E g + E int Amount of Energy Transferred = Change in Energy Stored W = ∆E total = ∆E k + ∆E el + ∆E g + ∆E int WITHIN the system External to the system

4. Tote bag demo  Draw a force diagram for the tote bag at rest  Draw a force diagram for the tote bag with a constant velocity

5. Tote bag demo – continued  When bag is lifted at a constant velocity, the lifting force (F LIFT ) is equal to the weight (mg) for the entire time.  Lifting an object, ADDS energy that is stored as E g (gravitational potential).  Work = energy added to system F LIFT F g = mg

6. Tote bag demo – continued  When bag is lifted at a constant velocity, the lifting force (F LIFT ) is equal to the weight (mg) for the entire time.  Work = energy added to system  Work = (F LIFT ) (height lifted) = (mg) (h) F LIFT F g = mg Work = (Force Applied)*(Distance Applied) Work = F ∆x

7. Working: Other Examples  Block pushed across floor = (F push )*( ∆x)  Block pushed with force of 200 N for 30 m  Work = (200 N)*(30 m) = 6000 J

8. Working: Other Examples  Work done on elevator lifted 100 m W = (F lift )*( ∆y)  Elevator with mass 1000 kg and weight 9800 N lifted 100 m  Work = (9800 N)*(100 m) = 980,000 J

9. Power

10. Power: Example  When doing a chin-up, a physics student with a weight of 480 N lifts her body a distance of 0.25 meters in 2 seconds.  How much work are the student’s muscles doing?  Work = Force (∆y) = (480 N)*(0.25 m) = 120 J  How much power are the student’s muscles supplying?  Power = Work / Time = 120 J / 2 sec = 60 Watts

12. Energy – and signs  Vectors… examples?  Velocity  Acceleration  Is energy a vector?  Hint: Is money a vector?  But, we DO use signs when talking about energy transfer… What do they mean?  + means energy transferred into the system  - means energy transferred out of the system

13. Working: Calculations  Work done on tote bag = Energy transferred to bag  W = ∆E k + ∆E el + ∆E g + ∆E int  Work = ∆E g = (F LIFT * h) = F* ∆y

14. Gravitational Energy (E g )

15. Working: Definition  Transfer of energy by an external agent applying a force parallel to the direction of motion  External – transfer of energy into or out of the system  Parallel – aligned with motion Ex: x-direction of motion

16. Basic Energy Model: 2 types of problems W = ∆ E total = ∆E k + ∆E el + ∆E g + ∆E int W = 0 W = ∆ E total

17. Tote bag demo – continued Area under a force (F) vs. displacement ( ∆ y) curve = energy  Spring Lab (E el ):  Lifting an Object (E g ): ∆ y

18. Working: Calculations  Energy transferred to, and then stored in, spring:  Area under F vs. ∆x graph  ∆ Energy = W = F * ∆x  Work is energy transferred during an interaction that results in a displacement of the point of application of the force

19. Energy Storage

20. Solving Other Problems  Changing gravitational energy to kinetic energy is useful for solving many different types of problems. Straight Ramps 1 Curved Ramps 11 2 Freefall Pendulums 22 1 2 h The speeds will be the same, but the directions different!

21. Mechanical Energy  In all instances, an object that possesses some form of energy supplies the force to do the work.  In all instances in which work is done, there is an object that supplies the force in order to do the work. In the instances described here, the objects doing the work (a student, a tractor, a pitcher, a motor/chain) possess chemical potential energy stored in food or fuel that is transformed into work. In the process of doing work, the object that is doing the work exchanges energy with the object upon which the work is done. When the work is done upon the object, that object gains energy. The energy acquired by the objects upon which work is done is known as mechanical energy.Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position kinetic energypotential energy  An object that possesses mechanical energy is able to do work. In fact, mechanical energy is often defined as the ability to do work. Any object that possesses mechanical energy - whether it is in the form of potential energy orkinetic energy - is able to do work. That is, its mechanical energy enables that object to apply a force to another object in order to cause it to be displaced.potential energykinetic energy  A dart gun is still another example of how mechanical energy of an object can do work on another object. When a dart gun is loaded and the springs are compressed, it possesses mechanical energy. The mechanical energy of the compressed springs gives the springs the ability to apply a force to the dart in order to cause it to be displaced. Because of the springs have mechanical energy (in the form of elastic potential energy), it is able to do work on the dart. Mechanical energy is the ability to do work.potential energy

22. Mechanical Energy: Conserved

23. Whiteboard Problem  How high should the cart be placed so that it will have a velocity of 1m/s when it goes through the photogate? (Photogate) h = ? h = 0m m = 0.291kg