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Introduction to Work & Energy

Introduction to Work & Energy. Introduction to work and energy | Work and energy | Khan Academy ( 9 min). Work, W. W = F ∙ d F and d: vectors F and d must be in the same dimension If F and d have the same direction, W = + If F and d are in opposite direction, W = ‒

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Introduction to Work & Energy

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  1. Introduction to Work & Energy • Introduction to work and energy | Work and energy | Khan Academy ( 9 min)

  2. Work, W • W = F∙d • F and d: vectors • F and d must be in the same dimension • If F and d have the same direction, W = + • If F and d are in opposite direction, W = ‒ (Ex) Work done by kinetic friction • If F and d are perpendicular to each other, W = 0 • W: a scalar quantity • Units of work: N·m = joule (the same as energy)

  3. A common mistake W= Fd Wy Wx Wx ≠ Fdcosө Wy ≠ Fd sin ө θ

  4. Work done at an angle F d dy dx Wx (assume no frictional force) = Fxdx = (F·cosθ)dx = (F·cosθ)(d·cosθ) Wy(assume no gravitational force) = Fydy = (F·sinθ)·dy = (F·sinθ)· (d·sinθ) θ

  5. Work done when force applied at an angle F dy dx Wx (assume no frictional force) = Fxdx = (F·cosθ)dx Wy(assume no gravitational force) = Fydy = F·sinθ·dy θ

  6. Determine W in each

  7. Diagram Answers • W = (100 N) * (5 m)* cos(0 degrees) = 500 J • W = (100 N) * (5 m) * cos(30 degrees) = 433 J • W = (147 N) * (5 m) * cos(0 degrees) = 735 J

  8. Example, Pg 169 How much work is done on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30.0˚ above the horizontal?

  9. Example A sailor pulls a boat a distance of 30.0 m along a dock using a rope that makes a 25.0˚ angle with the horizontal. How much work does the sailor do on the boat if he exerts a force of 255 N on the rope? Use this example for #3 of Work Problems WS

  10. Force vs. Displacement Graph • The area under the graph = work

  11. Work and Motion • Doing work consumes energy • Work done by an object = –W = object loses energy • If negative W changes the object’s speed, it slows down. • Slowing down = Directions of a and v are opposite = Directions of F and v are opposite • Work done becomes energy • Work done on an object = + W = object gains energy • If positive W changes the object’s speed, it speeds up • Speeding up = Directions of a and v are the same = Directions of F and v are the same.

  12. Examples Positive work or negative work? • The road exerts a friction force on a speeding car skidding to a stop. • A rope exerts a force on a bucket as the bucket is raised up a well. • Air exerts a force on a parachute as the parachute slowly falls to Earth. • The Earth exerts a force on a bobsled as it moves down a track.

  13. Example A worker pushes a 1.50×103 N crate with a horizontal force of 345 N a distance of 24.0 m. Assume the coefficient of kinetic friction between the crate and the floor is 0.220. • How much work is done by the worker on the crate? (b) How much work is done by the floor on the crate? (c) What is the net work done on the crate?

  14. Forms of Energy • kinetic energy • potential energy • gravitational • elastic/spring • chemical energy = stored energy • electrical energy *The units for all forms of energy: N·m = joule *Energy and work are interchangeable (Work is considered as a form of energy)

  15. Kinetic Energy, KE • Work done on an object causes the object’s velocity change from 0 to v • Work-Energy theorem W = ∆KE • Don’t understand as W = KE

  16. Example 5B, Pg 173 A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have? How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball?

  17. Example A skater with a mass of 52.0 kg moving at 2.5 m/s glides to a stop over a distance of 24.0 m. (a)How much work did the friction of the ice do to bring the skater to a stop? (b) How much work would the skater have to do to speed up to 2.5 m/s again?

  18. Potential Energy • Gravitational • Gravitational Potential Energy – YouTube (8 mn) • Spring • http://www.youtube.com/watch?v=ZzwuHS9ldbY (10 min)

  19. Gravitational Potential Energy, gPE • Work done against the gravitational force is stored as energy • Work done against gravitational force : • Fg = Fapp • Fnet = 0

  20. Gravitational Potential Energy, gPE • PEg = Fg∙d = mgh • m = mass • g = 9.8 m/s2 • h = height distance • ∆PE = mg(hf – hi)

  21. Example You lift a 7.30-kg bowling ball from the storage rack and hold it up to your shoulder. The storage rack is 0.610 m above the floor and your shoulder is 1.12 m above the floor. • When the bowling ball is at your shoulder, what is the bowling ball’s PEg relative to the floor? • When the bowling ball is at your shoulder, what is the PEg relative to the storage rack? • How much work was done by gravity as you lifted the ball from the rack to shoulder level?

  22. Elastic Potential Energy, PEelastic • PEelastic = (1/2) kx2 • k = spring constant • x = displacement • FYI:

  23. Example Find the elastic potential energy stored in a drawn bow if it takes an average force of 100N to pull the arrow back a distance of 0.5 meters.

  24. Example, Pg 176 A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0 m. When he finally stops, the cord has a stretched length of 44.0 m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?

  25. Conservation of (Mechanical) Energy • Mechanical energy, ME = KE + PE • Assumes there is no other type of energy • Energy can transform: KE ↔ PE • KEbefore + PEbefore = KEafter + PEafter • http://ww.physicsclassroom.com/mmedia/energy/ie.cfm • In reality, some ME transforms to thermal energy (=heat), sound energy, etc • In car collisions • In inelastic collisions (soft, sticky material)

  26. Find the missing energies

  27. Graph of KE, PE, ME Describe the motion of an object (A) (B)

  28. Problem-Solving Strategy • Determine the KE and PE before and after an event • Set KEbefore + PEbefore = KEafter + PEafter • Don’t use if there is other types of energy • Solve for and check the answer

  29. Example, Pg 181 Starting from rest, a child zooms down a frictionless slide with an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg.

  30. Example, Pg 185 On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

  31. Work-Energy theorem • W = ∆KE • Don’t understand as W = KE • Work becomes kinetic energy; kinetic energy becomes work

  32. Power, P • how fast work is done = work done per second • unit of P = watts (W); Don’t confuse watts with work W • 1 W = 1J/s = 1 joule of work done in 1 sec • 1 HP (horse power) = 746 W

  33. Example, Pg 188 A 193 kg curtain needs to be raised 7.5 m in as close to 5.0 s as possible. Three motors are available. The power ratings for the three motors are listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job?

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