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Work and Energy

Work and Energy. So far, we have viewed motion in terms of Newton’s 3 Laws. What are they?. Law of Inertia – a body at rest stays at rest & a body in motion continues in its straight line motion at a constant v unless a net external force acts on it.

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Work and Energy

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  1. Work and Energy So far, we have viewed motion in terms of Newton’s 3 Laws. What are they?

  2. Law of Inertia – a body at rest stays at rest & a body in motion continues in its straight line motion at a constant v unless a net external force acts on it.

  3. Law of Acceleration -An Fnet will cause a mass to accelerate F = ma.

  4. Action- Reaction - If a force is applied to a particle by a body, the particle will apply an equal but opposite force to the body.

  5. Work, Power, & Energy Energy, E offers an alternative analysis of motion and its causes. Changes in E is valuable in analyzing motion in systems i.e. roller coasters, engines, power plants, transformers. What are some types of energy? What is energy? Define it.

  6. Def: Energy is ability to do work. Work is done when force applied to an object or particle causes motion parallel to force direction. Work and Energy are Scalar quantities.

  7. W = F net x d cosq. • F = parallel l lto displacement N. • .q = angle between force and displacement. • .q = 0, W = Fd. • d = displacement – m. • If Faphas no component parallel to motion W=0! • Remember Fnet= S F, if more than 1parallel force, they add.

  8. Units W = Fd = (N m) kg m m . s2kg m2.s2 Joules (J)

  9. When a force F is applied to an object, it may produce a displacement d.

  10. Work can be zero even if force is applied.W = Fd cos a • The work done is zero if: • d = 0 m (no displacement) • force perpendicular to the displacement.

  11. Work is Scalar but: Work is positive when the force component causing the displacement is in the same direction as the displacement.

  12. Work is negative when the force component causing the displacement is in the opposite direction as the displacement.

  13. Zero Work • There are many important examples of forces that do not do any work. • For example, the gravitational force between the earth and the moon does not do any work!

  14. Moving horizontally while applying an upward force is not work. Yeah – right!!

  15. Examples W = Fd • How much work is done to lift a 10 N chair 1 meter? • How much work is done to hold a 44 N weight at a constant height of 2.0 m? 10N x 1m 10-J 44N x 0 W = Fd W = 0

  16. Forces acting at angles to motion Consider the Force Component parallel to displacement.

  17. Ex 1: A man pulls a cart with a ropethat makes a 20o angle to the horizontal. If he exerts a 100 N force, how much work is done is he pulls the cart 8.0 meters?

  18. W = F cos q d = 100 N (cos 20o)(8.0m) = 752 Nm = 752 J 100 N 20o FII

  19. Ex 2. A student lifts a 1.5-kg box 2-m straight up. a. How much work did she do on the box? b. How much work did gravity do on the box?

  20. The force on the box was:Fg = mg (1.5 kg)(10 m/s2) = 15-N.The work done by the student was W = Fd (15-N)(2-m) = +30 J.Gravity did negative 30 J of work b/c it was pulling in the opposite direction of the displacement.

  21. Hwk: Worksheet “intro work” • Hwk Work Prb’s Text read 168 – 171 • Do 170 all • Pg 193 #2, 3, 4, 5, 7-9.

  22. Hwk Work Prb’s Text read 168 – 171 • Do 170 all • Pg 193 # 3, 4, 5, 7-9.

  23. Energy

  24. Energy = Ability to do work.Energy is measured in Joules. E measured in terms of amount of work it can do. If a battery has 9 J of E, it can do 9 J of work.

  25. Relationship between Work and Energy. • It takes work to change an object’s energy from one form to another, or to increase or decrease it. • What are some forms of energy?

  26. Common Energy Types:Kinetic (KE) – energy of motionGravitationalPotential (GPE) – energy due to height in gravitational field.Chemical- energy stored in chemical bondsElasticPotential – energy stored in shape deformations.

  27. ElectricalEnergy – due to charge separation.Internal or HeatEnergy (Q) – due to vibration of atoms.Mass/NuclearEnergy = Stored between subatomic particles. E = mc2.

  28. Kinetic Energy, KE is energy associated with object in motion. The amount of KE = ½ mv2. m = mass in kg. v = velocity in m/s. KE in Joules (J) or Nm.

  29. Derivation of KE equation. • KE = W • KE = FDd • KE = maDd • KE = m (Dv)Dd = m Dv Dd Dt Dt = m Dv v = m(vf - vi) (vf + vi) where vi = 0 2 KE = ½ mv2.

  30. Ex 3: Calculate the speed of a 80,000-kg airplane with KE = 1.1 x 109 J.

  31. KE = ½ mv2 = 170 m/s

  32. Work must be done to change the E of an object. W = DKE. W = KEf - KEi

  33. Ex 3: A pitcher does work to accelerate a 145g baseball from rest to 25 m/s.a) What is its KE?b) How much work was done to reach this speed?

  34. KE = 1/2mv2. • a) ½(0.145kg)(25m/s)2 = 45 J • b) since the KE is 45 J and the initial KE was zero: • DKE =KEf – KEi • DKE = 45 J – 0 J = 45 J of work

  35. Work – KE Theorem Wnet = DKE In order to change the velocity of an object (DKE), work must be done. The amount of work done is equal to the change in KE.

  36. Ex 4: How much work is required to accelerate a 1000 kg car from 20 m/s to 30m/s?

  37. The work needed is equal to the DKE. • DKE = KE2- KE1. • W = 1/2mv2f - 1/2mv2i. • =1/2(1000kg)(30m/s)2 -1/2(1000kg)(20m/s)2. = 2.5 x 105 J.

  38. Ex 4: On a frozen pond, a person kicks a 10-kg sled giving it an initial speed of 2.2 m/s. It slides and eventually comes to a stop. • How much work is done bringing it to a stop? • What force does work to stop the sled? • How far will the sled move after being kicked if the coefficient of kinetic friction is 0.10 between the ice and the sled?

  39. Listm = 10kg vi = 2.2 m/s vf = 0 m = 0.1d = ? W = DKE = KEf – KEi W = 0 - 1/2mvi2. W = ½(10kg)(2.2)2.= 24.2 J Friction stops the sled.

  40. W = 24.2 J • Fd = 24.2 J • mFnd=24.2 J • mmgd = 24.2 J • 0.1(10kg)(9.81m/s2)d = 24.2 J • d = 2.48 m.

  41. In the past we’ve used velocity, acceleration equations to solve for distance, velocity etc. We can consider using KE and work equations.

  42. Text Pg 176 #1, 2, 4 and • pg 193 #5-10 12-14.

  43. Force/distance GraphsArea under curve = work or DE.

  44. Do Now: A constant force is applied over a distance to an object & graphed. How would we calculate work from the graph? Find the work done at 8-m.

  45. What if the force is not constant but varies over distance? How would we find the work done from the graph? Find the work done between 4 – 8m. ½ (4mx5N) = 10 Nm Wtot = 20+10=30 Nm 4mx5N = 20 Nm

  46. How much work between 8 – 14 m? • 25J

  47. Potential Energy – Stored Energy An object can store energy as the result of its position.

  48. Gravitational Potential Energy (GPE or PEg) Energy due to position of object above some base level (lowest available point).

  49. PEg = work done to raise some distance against gravity. W = Fd W = mgd PEg = mgDh

  50. Examples of work done by GPEPile driver Dam or waterfallsSee Saw Circus Act.

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