Last Thoughts on Work

2. Last Thoughts on Work • Work can be done by friction • Friction always opposes motion so the work it does is usually negative. (exceptions are like conveyor belt.) • Friction is a “dissipative force.” Turns Mech. Energy into another form: • often useless heat. • Sometimes called non-conservative force, since it doesn't conserve mechanical energy.

3. Kinetic Energy • Energy associated with the motion of an object • Scalar quantity with the same units as work • Work is related to kinetic energy

4. K.E. Is not momentum p = momentum p = mv p is a vector p is always conserved in a closed system. Always. Always. Always. K.E. = 1/2mv2 K.E. Is a scalar K.E. Is not always conserved. It can turn into any other form of energy.

5. Work-Kinetic Energy Theorem • When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy • Speed will increase if work is positive • Speed will decrease if work is negative

6. Work and Kinetic Energy • An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest • The moving hammer has kinetic energy. • The hammer will be doing work on the nail.

7. Types of Forces • There are two general kinds of forces • Conservative • Work and energy associated with the force can be recovered. • (Usually means all the energy stays as some form of mechanical energy. Put ME in to the system and get ALL the ME out.) • Nonconservative • The forces are generally dissipative and work done against it cannot easily be recovered

8. More About Conservative Forces • Examples of conservative forces include: • Gravity (Roller Coaster, lift a brick) • Spring force (Pull a spring) • Electromagnetic forces (Magnetic crane at junk yard lifting a car) • Potential energy is another way of looking at the work done by conservative forces

9. Conservative Forces • A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points • The work depends only upon the initial and final positions of the object • Any conservative force can have a specific potential energy for each point in space. • (move brick straight up 2 feet. 2nd. Spin around in circles and move brick up 2 feet.)

10. Nonconservative Forces • A force is nonconservative if: The work it does is path dependent. • Examples of nonconservative forces • Kinetic friction, air drag.

11. Friction Depends on the Path • Which path loses more energy to friction? • Red or Blue?

12. Friction Depends on the Path • Which path loses more energy to friction? • Red or Blue? • Red, because the path is longer. • Pushing the book backwards across the table won't give you the energy back.

13. Potential Energy • Potential energy is associated with the position of the object within some system • Potential energy is a property of the system, not the object. • Assuming no friction, ME of the system is constant. It can transfer from one object to another in the system.

14. Work and Potential Energy • For every conservative force, a potential energy is associated with each position. • Think about a projectile. When the object falls, it “gets the energy back” that went into elevating it. • (Royals hitting a foul ball up into top deck vs ball falling back down to 1st row.)

15. Reference Levels for Gravitational Potential Energy • A location where the gravitational potential energy is zero must be chosen for each problem • The choice is arbitrary since the change in the potential energy is the important quantity • Choose a convenient location for the zero reference height • Often the Earth’s surface • May be some other point suggested by the problem • Once the position is chosen, it must remain fixed for the entire problem. • (Go back to Royals picture. Where does problem suggest as Frame of Ref? 3 good choices, bat height, top of flight, ground, but could do anything such as center of the earth.)

16. Reference Levels • At location A, the desk may be the convenient reference level • At location B, the floor could be used • At location C, the ground would be the most logical reference level • The choice is arbitrary, though, • it must remain fixed for the entire problem.

17. Conservation of Energy, cont. • Total mechanical energy is the sum of the kinetic and potential energies in the system. • ME = KE + PE of any point in the system. • Equation: ME = KE + PE = constant • This is only valid in the • absence of friction!

18. Below the Line write: 1.) Equation for ME. 2.) Equation for KE. 3.) Equation for PE. MEMORIZE these for the test. Additional Questions: 1.) Above KE everywhere, add v = 2.) Above v = everywhere, add ME= 3.) What is mass?

19. Problem solving strategy: • “Where did the energy start out?” • “How much of it was changed?” • --(work) • “Where did the energy end up?” • Did the path matter?

20. Discuss: Where is work positive and negative and relate it to velocity of skier.

21. The Work-Energy Theorem and Kinetic Energy Example 4 Deep Space 1 The mass of the space probe is 474-kg and its initial velocity is 275 m/s. If the 56.0-mN force acts on the probe through a displacement of 2.42×109m, what is its final speed?

22. The Work-Energy Theorem and Kinetic Energy

23. 6.2 The Work-Energy Theorem and Kinetic Energy

24. The gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?

25. Gravitational Potential Energy

26. Example 11 Fireworks A bottle rocket is set off. It flies upwards 29 m from it’s original height, and the propellant supplies 425 J, what is the final speed of the rocket. Ignore air resistance. Mass = .2kg

27. Nonconservative Forces and the Work-Energy Theorem