Ch. 5 Work and Energy

1. Ch. 5 Work and Energy

2. 5-1 Work • W = F X d • Wnet = Fnetd(cos θ) • Work (J) Force (N) distance (m) • Work is NOT done on an object unless it moves

3. Work is only done when the force is parallel to the movement of the object • W = F X d (cos θ) • Cos θ = 1

4. Work is a scalar quantity with a (-) or (+) • Sign depends on the force and direction

5. If force is in the direction of motion, then (+) work • If the force opposes motion, then (-) work • If the force is 90° to the motion, then no work

6. If the object is not in motion, then no work • If the object speeds up, then (+) work • If the object slows down, then (-) work

7. Sample Problem 5A

8. 5-2 Energy Kinetic Energy- energy associated with motion KE dependes on speed and mass KE = ½ mv2

9. ΔKE = ½ mvf2 – ½ mvi2 • KE is a scalar quantity-The SI unit is Joules (J) • Two objects traveling at the same speed, The object with the most mass will have more KE • Ex: 18 wheeler vs bicycle

10. In order to use a formula for net work, we need to use all forces that do work on the object • Net work (+) = speed increases • Net work (-) = speed decreases • Kinetic energy is the work an object can do

11. Work-Kinetic Energy Theorem • Wnet = ½ mvf2 – ½ mvi2 • Wnet = ΔKE • Wnet = Fnetd(cos θ)

12. Potential Energy • Potential Energy is stored energy because of its position relative to some other location. • Gravitational Potential Energy-energy due to an object’s position relative to a gravitational source

13. PEg = mgh • Gravitational potential energy turns into kinetic energy • SI unit for GPE is Joule (J) • GPE depends on the height and free fall acceleration of an object • GPE is a result of an object’s position so it must be measured relative to some zero level.

14. Elastic Potential Energy • Elastic Potential Energy-stored energy in a stretch or compressed spring • Relaxed length-the length of a spring with no external forces acting on it • The amount of energy depends on the distance the spring is compressed or stretched from the relaxed length.

15. PEelastic = ½ kx2 • K is the spring constant or force constant • X is the distance the spring is stretched or compressed • Flexible spring, k is usually small • Stiff spring, k is large • Unit for spring constant is N/m

16. 5-3 Conservaton of Energy • Conservation means we have a constant amount but it can change forms • Ex: mass • Motion of objects involves a combination of kinetic and potential energy • We will ignore other forms of energy because they have very little influence on the motion of objects

17. Mechanical energy-the sum of kinetic energy and all forms of potential energy • ME = KE + ΣPE • Nonmechanical energy = all energy not mechanical such as nuclear, chemical, internal, and electrical

18. Mechanical energy is often conserved in the absence of friction but it can change forms • Potential energy is continuously converted into kinetic energy and back into potential energy

19. Conservation of Mechanical Energy • MEi = MEf • Substituting Peg and KE into the formula: • ½ mvi2 + mghi = ½ mvf2 + mghf

20. Also, add PEelastic (1/2 kx2) into both sides if the situation also has a spring

21. Conservation of mechanical energy will not hold true with friction because not all kinetic energy is converted back to potential energy. • Energy conservation occurs even when acceleration varies as long as friction can be ignored.

22. Friction: Kinetic energy is converted to nonmechanical energy (heat) so mechanical energy (KE and PE) is no longer conserved. • Total energy is always conserved

23. 5-4 Power • Power-the rate at which work is done or the rate energy is transferred • Power= Work/Time Interval • P = W/Δt

24. Alternative Formulas • P = Fd/Δt because W = Fd or P = mgd/Δt • P = Fv because d/Δt = v

25. SI unit of Power is Watt (W) • 1 W = 1 J/s • Another unit of power is horsepower (hp) • 1 hp = 746 Watts

26. Different power ratings do the same work in different time intervals