Work, Energy, Power

1. Work, Energy, Power

2. What’s the difference? • Force is the agent of change • Energy is a measure of change • Work is a way of transferring energy from one system to another

3. What is work? • Work= force*displac. • W=Fd • Only work if there is motion- if you push against a brick wall and it doesn’t move, you might be tired but you have done no work • Unit=Joule (unit of energy)

4. Are they work? • No- no displacement • Yes- force=g and displacement=fall • No-why? • Yes- force from engines • Teacher pushes wall and becomes exhausted • Book falls off table to floor • Waiter carries large tray across restaurant at constant v • Starship Enterprise accelerates through space So what’s with the waiter???????

5. Work = 0 • Work = 0 if: • No force • No displacement • force is perpendicular to displacement

6. Power • Power= rate at which work gets done= work over time • P=W/t • Since W=Fd then P=Fd/t and d/t=v • P=Fv • Unit= J/s=watt (W) • Careful not to confuse unit W (watt) with concept W (work)

7. Ex: Power • A mover pushes a large crate mass=75kg across the truck bed for a total distance of 6m. He exerts a steady force of 300N for 20s. What is his power output? • P=W/t P=Fd/t=(300N)(6m)/20s=90W

8. Kinetic Energy • Energy of MOTION • K=1/2mv2

9. Example… • Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s • KE = (1/2)*m*v2 • KE = (0.5) * (625 kg) * (18.3 m/s)2 • KE = 1.05 x105 Joules

10. Potential Energy=U Energy an object has due to its position or configuration- stored energy that can be retrieved. Ex- height on a wave gives U, pulling back the string on a bow gives it U, compressing or stretching a spring gives U.

11. Potential Energy: Energy of POSITION

12. Gravitational Potential Energy: Ug • Potential energy due to position relative to surface of the earth • Ug=mgh • Unit = Joule

13. Gravitational Potential Energy: Ugand Work done by gravity • Gravity can do + or - work depending on motion • Path independent- depends on height, not path taken • Wg=mgΔh • Where h is height above arbitrary 0 pt

14. Examples • Physicsman (mass=60kg) scales a 40m tall rock face. What is his potential energy (relative to the ground)? • Ug=mgh=(60kg)(10N/kg)(40m)=24000J

15. Mechanical Energy: U and K:Energy because of position or motion

16. Total Mechanical Energy is CONSERVED PE ONLY PE + KE KE ONLY

17. Take it 1 step further… • If physicsman (60kg) were to jump of the cliff (remember his U=24000J), what would his velocity be when he hits the ground? Think…U is transformed to K • At the top he has all U=24000J • At the bottom he has all K=1/2mv2 • Utop=Kbottom • 24000J=1/2(60kg)v2 • V=28m/s

18. Work by Conservative vs. Nonconservative Forces • Conservative forces are path independent • Ex: gravity • Nonconservative forces depend on path • Ex: kinetic friction- longer path means more work

19. Work and Energy • E=K+U • E=1/2mv2+mgh • Object’s mechanical energy is sum of kinetic and potential energies • Since U is relative to position, so is E • Wnc=ΔK+ΔU • Work done by nonconservative forces is sum of changes in K and U

20. Conservation of Energy • Since E=K+U, if no nonconservative forces (friction for example) act on a system then mechanical energy is conserved • Ei=Ef • Ki+Ui=Kf+Uf

21. Ex: conservation of energy • A ball of mass 2kg is gently pushed off the lab table, 5.0m above the floor. Find the speed of the ball as it strikes the floor • Ei=Ef or Ki+Ui=Kf+Uf • 0+mgh=1/2mv2+0