1. Chapter 5 Work, Energy, and Power

2. Work W = F x This equation applies when the force is in the same direction as the displacement are in the same direction

3. A linebacker pushes against the blocker but the blocker does not move. The work is: 1. Positive 2. Negative 3. Zero 4. Not enough info Answer Now

4. When doing a bench press, you gradually lower the bar down to your chest. The work done by you is: 1. Positive 2. Negative 3. Zero 4. Not enough info Answer Now

5. When doing a bench press, you gradually lower the bar down to your chest. The work done by gravity is: 1. Positive 2. Negative 3. Zero 4. Not enough info Answer Now

6. When doing a curl, you exert a force to raise the dumbbell to your shoulder. The work done by you is: 1. Positive 2. Negative 3. Zero 4. Not enough info Answer Now

7. Because your two-year old cousin refuses to move, you pull him along the ground while tugging at an angle. The work done is: 1. Positive 2. Negative 3. Zero 4. Not enough info Answer Now

8. If there exists a force on an object an the object moves, work must have been done. 1. True 2. False

9. Work Can Be Positive or Negative Work is positive when lifting the box Work would be negative if lowering the box The force would still be upward, but the displacement would be downward

10. When Work is Zero Displacement is horizontal Force is vertical cos 90° = 0

11. Units of Work SI Newton meter = Joule N m = J J = kg m 2 / s 2

12. Work W = (F cos )x  is the angle between If  = 0, cos  = 1, and W = F Δx If  = 90 o, cos = 0, and W = 0

13. More About Work The work done by a force is zero when the force is perpendicular to the displacement cos 90° = 0

14. Limitations of Work This gives no information about: the time it took for the displacement to occur -or- the velocity or acceleration of the object

15. Work is a Scalar Even though the sign matters (like vectors), the sign does not indicate the direction if travel.

16. Let’s try some practice problems:

17. Kinetic Energy Energy associated with the motion of an object Scalar quantity measured in Joules

18. Work-Kinetic Energy Theorem The net work done on an object 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

19. Gravitational Potential Energy Gravitational potential energy is associated with the vertical position of the object PE grav = mgy y = vertical position (relative to a reference point – usually ground) g = acceleration due to gravity

20. Conservation of Mechanical Energy Total mechanical energy is the sum of the kinetic and potential energies in the system and is stays constant (if closed system)

21. On which track does the marble have the largest initial potential energy? 1. Green 2. Yellow 3. Red 4. Blue 5. All the same

22. On which track will the marble have the largest final velocity? 1. Green 2. Yellow 3. Red 4. Blue 5. All the same

23. On which track does the marble have the largest total mechanical energy at the beginning? 1. Green 2. Yellow 3. Red 4. Blue 5. All the same

24. If a steel marble is released down the green track and a plastic marble goes down the blue track, which will have the greater velocity at the end of the track? 1. Steel 2. Plastic 3. Same

25. If a steel marble is released down the green track and a plastic marble goes down the blue track, which will have the greater kinetic energy at the end of the track? 1. Steel 2. Plastic 3. Same

26. On which track did the marble have the largest average velocity? 1. Green 2. Yellow 3. Red 4. Blue 5. All the same

27. On which track did the marble have the second largest average velocity? 1. Green 2. Yellow 3. Red 4. Blue 5. All the same

28. Notes About Conservation of Energy We can neither create nor destroy energy Another way of saying energy is conserved If the total energy of the system does not remain constant, the energy must have crossed the boundary by some mechanism (friction, heat, sound, …)

29. When graphing F vs. –x, what was the relationship? 1. Linear 2. Quadratic 3. Power Function 4. Inverse 5. No relationship

30. Springs – Hooke’s Law One of the simplest type of simple harmonic motion is called Hooke's Law. This is primarily in reference to SPRINGS. The negative sign only tells us that “F” is what is called a RESTORING FORCE, in that it works in the OPPOSITE direction of the displacement.

31. Hooke’s Law F elas = -kx F elas = Elastic force of the spring (force points back to equilibrium position.) (N) k = Spring constant (N/m) x = displacement from equilibrium (m) (note:opposite to direction of the elastic force)

32. Hooke’s Law from a Graphical Point of View x(m)Force(N) 00 0.112 0.224 0.336 0.448 0.560 0.672 Suppose we had the following data: k =120 N/m

33. We have seen F vs. x Before!!!! Work or ENERGY = F  x Since WORK or ENERGY is the AREA, we must get some type of energy when we compress or elongate the spring. This energy is the AREA under the line! Area = ELASTIC POTENTIAL ENERGY Since we STORE energy when the spring is compressed and elongated it classifies itself as a “type” of POTENTIAL ENERGY, U s. In this case, it is called ELASTIC POTENTIAL ENERGY.

34. Elastic Potential Energy The graph of F vs.x for a spring that is IDEAL in nature will always produce a line with a positive linear slope. Thus the area under the line will always be represented as a triangle. NOTE: Keep in mind that this can be applied to WORK or can be conserved with any other type of energy.

35. Elastic potential energy Elastic “potential” energy is a fitting term as springs STORE energy when there are elongated or compressed.

36. Conservation of Energy in Springs

37. Strain PE vs. Gravitational PE The area under the curve on the left equals the energy stored in a linear spring, or the amount of work required to deform the spring. The area under the curve on the right equals the potential energy due to the constant force of gravity (mg), or the work required to lift an object x m. Note that one area is square and the other triangular. Force (N)  x (m) 0 Strain Force (N) “mg”  x (m) “h” 0 Gravitational ½F  x F  x or mgh

38. Power Often also interested in the rate at which the energy transfer takes place Power is defined as this rate of energy transfer SI units are Watts (W)

39. Power, cont. US Customary units are generally hp Need a conversion factor

40. Work is done when 1. the displacement is not zero. 2. the displacement is zero. 3. the force is zero. 4. the force and displacement are perpendicular.

41. If both the mass and the velocity of a ball are tripled, the kinetic energy of the ball is increased by a factor of 1. 3. 2. 6. 3. 9. 4. 27.

42. Of the following examples, the one that represents work as defined by a scientist is: 1. lifting a book from your desk. 2. leaning on a shovel while others labor. 3. pushing hard against a wall for an hour. 4. carrying a heavy box on your head.

43. The ability to do work is defined as: 1. force and measured in joules. 2. energy and measured in watts. 3. power and measured in watts. 4. energy and measured in joules.

44. A rolling wagon has 50 joules of kinetic energy. If the wagon’s velocity is doubled, the kinetic energy of the wagon: 1. is reduced to 25 joules. 2. is increased to 100 joules. 3. is increased to 200 joules. 4. remains the same.