Work & Energy Day #1: Introduction

1. Work & EnergyDay #1: Introduction Hw: Handout #1 Turn in HW Packet from Forces Unit: (5 HW Handouts) Essay due Wednesday…

2. I. A. Define Work: Work is a measure of what is accomplished when a force is applied onto an object while the object moves. The object must be moving while the force is applied. B. Equation of work: Work is defined as the product of the force applied on an object and the displacement of the object.

3. F = force acting on the object Dx = displacement of the object The angle q is the angle between the direction of the force F and the displacement Dx.

4. C. Units for work: The product of force and displacement gives units of newtons times meters. This unit is given a special name: joule = J The relationship is given as follows:

5. D. Alternate expression for work: The term F||=Fcosq is the component of the force F that is parallel to the displacement Dx. The work is the product of these two parallel components.

6. E. Work and sign (±): For the equation of work on the left, there is a dependence on the direction of the force relative to the displacement. If 0o ≤ q < 90o, then the work is positive. If 90o < q ≤ 180o, then the work is negative. If F|| points in the same direction as the displacement Dx, then the work is positive. If F|| points in the opposite direction as the displacement Dx, then the work is negative.

8. Ex. #1: A 10.0 kg mass is pulled towards the right 10.0 m by an applied force of 40.0 N. The applied force also points towards the right and the object moves at a constant velocity. (a) Draw all the forces acting on the object. n = Normal Force Fk = Kinetic Friction Force Fo = Applied Force mg = Weight Dx = Motion

9. (b) What is the work done by the normal force? (c) What is the work done by the weight force of the object? General Rule: Any force applied perpendicular to the motion does not do any work!

10. (d) What is the work done by the applied force?

11. (e) What is the work done by the friction force? Fk = Kinetic Friction Force Fo = Applied Force Since the object moves at a constant velocity, the forces balance!

12. (f) What is the net work on the object? NOTE: Since the object moves at a constant velocity, the forces balance!

13. Ex. #2 Is it possible to do work on an object that remains at rest? Why of why not? NO. Work requires a displacement: Ex. #3: A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1) friction does no work at all 2) friction does negative work 3) friction does positive work Friction points opposite to the motion of the object!

14. Ex. #4: Can friction ever do positive work? YES! Consider a box placed on the back of a flatbed truck: Fs When the truck drives forwards, the inertia of the box makes the box appear to slide to the back of the truck. Friction between the box and the truck pulls the box forward, opposing its motion towards the back of the truck.

15. Ex. #5: In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work on the ball 2) catcher has done negative workon the ball 3) catcher has done zero workon the ball The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos q ), since q= 180o, thenW < 0. Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher?

16. Ex. #6: A man with a weight of 735 N stands in an elevator that accelerates upwards at 1.20 m/s2 for 5.00 m. (a) What is the work done by gravity? NOTE: Since the object moves upwards, and the weight points downwards, q = 180o. n = Normal Force mg = Weight

17. (b) What is the work done by the normal force? NOTE: Since the acceleration is given, solve for the normal force using Newton’s 2nd Law: The sum of the forces is: NOTE: the weight is given, not the mass!

18. NOTE: Since the object moves upwards, and the normal force points upwards, q = 0o.

19. Ex. #7: A block is pulled towards the right with a force of 50.0 N applied at an angle of 36.9o above the horizontal. The block is already in motion and moves a distance of 20.0 meters at a constant velocity. (a) What is the work done by the applied force? Fo n = normal q = 36.9o FK m mg = weight

20. (b) What is the work done by the force of friction? The object moves at a constant velocity, which means the forces balance. Friction will balance the horizontal component of the applied force. Note that the net work is zero when the velocity is constant.

21. (c) If the block has a mass of 12.0 kg, what is the coefficient of kinetic friction? Fo n = normal q = 36.9o FK m mg = weight

22. Ex. #8: A mass of 44.0 kg is pulled towards the top of a ramp at a constant speed by an applied force. The applied force is parallel to the ramp, and points towards the top of the ramp. The coefficient of friction between the ramp and the surface is 0.400 and the block is pulled a distance of 5.00 meters up the ramp. What is the work done by each force? What is the total work on the object? The angle of the incline is 30.0o.

23. The first step is to solve for each force: The ┴ forces balance: substitute From the definition of kinetic friction: substitute definition The net force parallel to the ramp is zero as well:

24. The work done by the normal force is zero: Calculate the work done by gravity through its components. Only the parallel component will do work.

25. The work done by the applied force is:

26. The work done by the friction force is: Finally, the total work done is:

27. Work & EnergyDay #2: Work Energy Theorem Hw: Handout #2 {back of notes packet}

28. Work Energy Theorem I. Introduction: A. What is energy? Energy is defined as the ability to do work. If an object has energy, then this object can perform work. Energy and work are two forms of the same overall concept.

29. B. What are the types of energy? 1. kinetic energy: Kinetic Energy is defined as energy associated with motion. Work can be done from the movement of an object. wrecking ball water wheel 2. potential energy: Potential Energy is defined as energy associated with position. Energy can be stored in an object by virtue of its position. pile driver #2 pile driver

30. C. Equation and units for kinetic energy: Definition of kinetic energy KE: follow the equation for units: work and energy are two parts of the same overall concept, therefore they share the same units

31. D. What is the work energy theorem? The work energy theorem states that the change of the kinetic energy of an object is equal to the total amount of work done on the object. Note: the net work can be found by either finding the sum of the work done by each individual force or by finding the work done by the net force.

32. II. Examples: Example #1: What is the kinetic energy of a 10.0 kg mass moving at 6.00 m/s? Ex. #2: What speed should a 2.50 kg mass have so that it has the same kinetic energy as the above example? fast solution: m and v2 are inversely proportional. implies so finally

33. Ex. #3: {on your own} If a third mass has a speed of 4.00 m/s, what should its mass be so that it has the same kinetic energy as that of problem #1?

34. Ex. #4: A force of 20.0 N pushes a 10.0 kg mass for a distance of 10.0 meters. The surface is frictionless. What is the speed of the object if it starts from rest?

35. Ex. #5: {on your own} How much force is needed to push a 4.00 kg mass from a speed of 5.00 m/s to a speed of 7.00 m/s in a distance of 5.00 meters?

36. Ex. #6: A mass of 10.0 kg is raised by a rope with a force of 110 N. a. What is the work done by this force if the mass is raised upwards 2.40 meters? b. What is the work done by gravity?

37. c. What is the net work on the object? Wnet > 0, object speeds up d. What is the speed of the object at the end of the motion if the mass starts from rest?

38. Ex. #7: A 4.00 kg mass has an initial upward velocity of 14.0 m/s. A cord is lifting upwards on the mass. If the mass slows uniformly to a stop in a distance of 40.0 meters, what is the lifting force?

40. Ex. 8: A 3000 kg car has an applied force of 2500 N moving the car forwards. At the same time, there is a 1500 N resistive force acting on the car. a. How much distance is needed to accelerate the car from 20.0 m/s to 25.0 m/s?

42. b. How much braking force is needed to slow the car from 25.0 m/s to a stop in a distance of 100 meters? What is the needed coefficient of static friction?

46. Ex. #9: If the speed of an object is doubled from speed v to speed 2v, what happens to the kinetic energy of the object? How does the distance compare for pushing the object from rest to speed v as compared to pushing the object from rest to speed 2v? implies so that For accelerating an object:

47. For accelerating from 0 → v: For accelerating from 0 → v compared to 0 → 2v: implies so that

48. Ex. #10: A 1.80-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 22.5 J at point B. What is (a) its kinetic energy at A? (b) its speed at point B? (c) the total work done on the particle as it moves from A to B?

49. Work & EnergyDay #3: Conservation of Energy Hw: Handout #3 {back of notes packet} Day #1: #2, 4, 6 – 10 all Day #2: #1, 3, 5, 13 Day #3: #17 – 22 all

50. Potential Energy and Conservation of Energy. I. Introduction. A. What is potential energy? Potential Energy is defined as energy associated with position. Energy can be stored in an object by virtue of its position.