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Work and Energy

Learn about work, energy, and their relationship through this comprehensive guide. Explore the equations, units, and different types of energy, and understand the principles of conservation and non-conservation of mechanical energy. With real-world examples and problem-solving techniques, this resource will help you grasp the complexities of motion and its connection to work and energy.

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Work and Energy

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  1. Work and Energy

  2. WHY…? • Curved paths (motion) • Complicated motion is tough to handle with just Newton’s Laws

  3. Definitions and Units • Contrary to what you might think, solving word problems is no longer considered “work” in this class, solving word problems will hereafter be referred to as “play” or “fun.” • Work, physical work, is an energy exchange, we will add it to a “system”…

  4. Work and Energy • Yes, we have equations for it… • Work = Force times distance • Or more appropriately the “dot” product of a force vector and the displacement vector of the object it acts on. • What are the units?

  5. Work and Energy • Joules! • You were probably thinking Newton’s times meters, huh? You are correct, we just have a special name for the units of work and energy. • Since work is an energy exchange, they both have the same units.

  6. Work and Energy • In the real world you can exchange dollars for doughnuts, but in the physical world it’s more like dollars for euros, yen, pounds(!) etc. • Work, kinetic, potential, heat, sound, light… • Let’s look at the dot product a little more…

  7. Work F q d Were interested in the component of force that actually moves the object in the direction it goes. The other component, perpendicular to the displacement, is “wasted.”

  8. Work Fcosq Fsinq F q d

  9. Work F q Fcosq d

  10. Work Yeah, memorize this one. F q Fcosq d

  11. Let’s Apply this puppy. Tleash angle displacement

  12. Puppy Pull • Ok, 1 – 2- 3 go • Tension in leash = 30 N • Angle with ground = 30 degrees • Displacement along the ground = 30 meters (this puppy is stubborn)

  13. So what’s the work? W= 30 N x 30 m x cos(30) = 779 Joules We did 780 joules of work on the puppy.

  14. Energy • So what is energy? • The physical state of an object that gives it the capacity to do work. • Ok, brass tacks time…

  15. Energy • You can probably mention two types, maybe more… • Kinetic • translational, rotational • Potential • gravitational, electrical, internal (temp) • Let’s just do Translational Kinetic and Gravitational Potential for now and save the others for later in this course.

  16. Kinetic Energy

  17. Work and KE Work Kinetic energy theorem

  18. Where’s this come from? • Think back to kinematics

  19. Apply! • My truck is broken down, so you help me push it. We give it a push of 300 Newtons, parallel to the road, and quit after 20 meters. How much work did we do, on the system (my truck)?

  20. How fast is it going? • Let’s ignore friction right now. The mass of the Miata is 750kg. Start from rest

  21. Video Break! • Big Truck

  22. Energy

  23. Potential Energy • Gravitational energy. • Let’s think this one through. If I lift 100 N one meter what work did I do? • Yeah, 100 Joules • How fast is it moving now? Yeah, nothin’ • What’s up? (besides the 100 N weight)

  24. PE • The energy went somewhere, where? • We say the weight gained Potential energy equal to the change in vertical position, altitude, or height, times its weight (the force it took to get it there). Yep.

  25. Work raising a weight • How much work is done raising a bucket from a well? • Bucket 10 kg • Well 20 meters deep • What work did the bucket raiser person do? • What work did gravity do?

  26. Conservative vs. Non-conservative forces Conservative – we can get it back So I lifted the 100N one meter, what happens when I drop it? It speeds up until it hits the ground. The work transforms into KE of the weight, so gravity is a conservative force.

  27. Conservative vs. Non-conservative forces Non-conservative Think back to the puppy pull. Let’s make it a box now, even though I did work on the box, friction also did work on the box. Due to Newton’s IIId law, friction did negative work on the box! What happens when we let go of the leash? Will the box spontaneously spring back to where it was? NO! Friction is non-conservative.

  28. Con vs non • Conservative forces store the energy when you work against them. You can get it back later. • Gravity, electrical force, springs. • Non-conservative Forces dissipate the energy of work done against them. You can’t get it back. It turns into; sound, heat etc. • Friction, airplane drag…

  29. Enough! • Let’s “play” • Conservation of mechanical energy Yeah, this one too.

  30. Block on a ramp • No friction • 10 kg block is 10 meters up on an incline. • It starts from rest and slides to the bottom • How fast is it going at the bottom? 10 kg 10 meters

  31. Fin. • Questions??

  32. Review

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