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Work, Power, & Energy

Work, Power, & Energy. Physics. Energy & Work. EQ 1: Who does more work?. Weight lifter #1- Benches 250 lbs one time over 22 inches Weight lifter #2- Benches 250 lbs one time over 18 inches. What is work?. In science, the word work has a different meaning than you may be familiar with.

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Work, Power, & Energy

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  1. Work, Power, & Energy Physics

  2. Energy & Work

  3. EQ 1: Who does more work? • Weight lifter #1- Benches 250 lbs one time over 22 inches • Weight lifter #2- Benches 250 lbs one time over 18 inches

  4. What is work? In science, the word work has a different meaning than you may be familiar with. The scientific definition of work is: applying a force to move an object a distance (force must be parallel to the direction.)

  5. Work is a Scalar Dot Product? A product is obviously a result of multiplying 2 numbers. A scalar is a quantity with NO DIRECTION. So basically Work is found by multiplying the Force times the displacement and… result is ENERGY, which has no direction associated with it. º = 1 A dot product is basically a CONSTRAINT on the formula. In this case it means that F and x MUST be parallel. To ensure that they are parallel we add the cosine on the end.

  6. Work

  7. Formula for work Work = FcosθΔx • The unit of force is newtons = N • The unit of distance is meters = m • The unit of work is newton-meters • One newton-meter is equal to one joule • So, the unit of work is a joule = J

  8. Pause for a Cause W = FcosθΔx Calculate: If a man pushes a concrete block 10 meters with a force of 20 N, how much work has he done? (W = 20N x 10m) = 200 Joules

  9. Work Example A 50 N horizontal force is applied to a 15 kg crate of granola bars over a distance of 10 m. The amount of work this force does is W = 50 N · 10 m = 500 N · m The SI unit of work is the Newton · meter. There is a shortcut for this unit called the Joule, J. 1 Joule = 1 Newton·meter, so we can say that the this applied force did 500 J of work on the crate. The work this applied force does is independent of the presence of any other forces, such as friction. It’s also independent of the mass. Tofu Almond Crunch 50 N 10 m

  10. *Pause for a Cause A vs B? • If the sled has a total mass of 50.0 kg, and the Eskimo exerts a force of 1.20x102 N by pulling the rope attached to the sled over a distance of 5.00 m… • A) How much work does he do if the rope is parallel to the ground? • B) How much work at angle θ = 30.0˚? does W = FcosθΔx A > B W = 1.20x102(cos0)(5) = 6.00E2 J W = 1.20x102(cos30.0˚)(5) = 5.20E2 Sum of the force in the y-axis = ?

  11. Work & Dissipative Forces • Doing work is nearly impossible without friction. • Ex: could you walk without friction? • Eskimo? • Friction cause energy to dissipate • Work done by friction

  12. *Pause for a Cause m = 50.0 kg, F = 1.20x102 N, x = 5.00 m, µk = 0.200 • C) How much work is done on the sled at cos0˚ • D) How much work is done on the sled at cos30.0˚ • C) 110 J Sum of the force in the y-axis = ?

  13. *Pause for a Cause Sum of the force in the y-axis = ? m = 50.0 kg, F = 1.20x102 N, x = 5.00 m, µk = 0.200 • C) How much work is done on the sled at cos0˚ • D) How much work is done on the sled at cos30.0˚ • D) 90.0 J

  14. Power: Work over time • W = FΔx Power: Power is the rate at which work is done. J s The unit of power is the watt. Power = Work Time P = W t P = maΔx t P = Fv W = maΔx  P = W t

  15. Pause for a Cause How much power will it take to move a 10 kg mass at an acceleration of 2 m/s/s a distance of 10 meters in 5 seconds? This problem requires you to use the formulas for force, work, and power all in the correct order. Force=Mass x Acceleration Work=Force x Distance Power = Work/Time

  16. Energy & Work

  17. Essential Question • EQ: What has more energy? • An object that has falling from 15 meters • Or an object resting 15 meters above the ground?

  18. Forms of Energy • The five main forms of energy are: • Heat • Chemical • Electromagnetic • Nuclear • Mechanical

  19. States of Energy • The most common energy conversion is the conversion between potential and kinetic energy. • All forms of energy can be in either of two states: • Potential • Kinetic • is stored energy. • the energy of motion. P.E. = mass x gravity x Height KE = mass x velocity2 2 Units of Energy mass x velocity2 Kg x (m/s)2 = Nm =J mass x gravity x Height Kg x m/s2 x m = Nm =J

  20. Energy Explanation • Energy is expressed in JOULES (J) • 4.19 J = 1 calorie • Energy can be expressed more specifically by using the term WORK(W) Work = The Scalar Dot Product between Force and Displacement. So that means if you apply a force on an object and it covers a displacement you have supplied ENERGY or done WORK on that object.

  21. Pause for a Cause • A 7.00 kg bowling ball moves at 3.00 m/s. How fast must a 2.45 g table tennis ball move in order to have the same kinetic energy as the bowling ball? Is this speed reasonable for a table-tennis ball in play? mb = 7.00 kg mt = 2.45 g vb = 3.00 m/s vt = ? 31.5 J 1.60E2 m/s

  22. Kinetic Energy Derived • Where does the formula for kinetic energy come from? • There are two ways to look at it. • 1st: Work + Newton’s laws of motion • 2nd: Work = Energy Smash together like terms Mind Blown!

  23. The Work Energy Theorem: Up to this point we have learned Kinematics and Newton's Laws. Let 's see what happens when we apply BOTH to our new formula for WORK! • We will start by applying Newton's second law! • Using Kinematic #3! • An interesting term appears called KINETIC ENERGY or the ENERGY OF MOTION!

  24. Work-Energy Theorem: not for notesF = max +Vf2 = Vi2 + 2aΔx Vf2 = Vi2 + 2aΔx  Vf2 - Vi2 =2aΔx Vf2 - Vi2 = aΔx  aΔx = Vf2 - Vi2 2 2 aΔx = Vf2 – Vi2W = maΔx 2 W = m Vf2 - Vi2 2

  25. Kinetic Energy Pause for a Cause KE = mv2 2 • A 4 kg rock is rolling 10 m/s. Find its kinetic energy. KE = • What has a greater affect of kinetic energy, mass or velocity? Why?

  26. Energy Derived: W = E not for notes (ΔX) (ΔX)

  27. Energy Derived

  28. Work-Energy Theorem Work Kinetic Energy Work-Energy Theorem Units

  29. Work-Energy Theorem Work Kinetic Energy Work-Energy Theorem

  30. The Work Energy Theorem And so what we really have is called the WORK-ENERGY THEOREM. It basically means that if we impart work to an object it will undergo a CHANGE in speed and thus a change in KINETIC ENERGY. Since both WORK and KINETIC ENERGY are expressed in JOULES, they are EQUIVALENT TERMS! " The net WORK done on an object is equal to the change in kinetic energy of the object."

  31. Pause for a Cause A 70 kg base-runner begins to slide into second base when moving at a speed of 4.0 m/s. The coefficient of kinetic friction between his clothes and the earth is 0.70. He slides so that his speed is zero just as he reaches the base (a) How much energy is lost due to friction acting on the runner? (b) How far does he slide? -560 J = 480.2 N 1.17 m

  32. Conservative & Nonconservative Forces • Forces are either conservative or nonconservative • Conservative • Energy is conserved • Ex: Gravity & springs • Rollarcoaster does work to reach the top • Nonconservative • Energy is lost (rendered unusable) • Ex: friction & heat • Car loses KE while applying brakes

  33. Gravitational Potential Energy • Stored energy due to position • “The bigger they are the harder they fall” is not just a saying. It’s true. Objects with more mass have greater G.P.E. • Potential energy that is dependent on position is called gravitational potential energy.

  34. Pause for a Cause:Calculate the potential energy of a 5 kg object sitting on a 3 meter ledge.

  35. Pause for a Cause How much PE does the skier have at point A? How much PE at point B? m = 60.0kg h =10 m

  36. Pause for a Cause How much KE does the skier have at point A? How much KE at point B? m = 60.0kg h =10 m

  37. Pause for a Cause What is the speed of the skier at point B? m = 60.0kg h =10 m 14 m/s

  38. Conservation of Energy • Energy can be neither created not destroyed by ordinary means • It can only be converted from one form to another. • If energy seems to disappear, then scientists look for it – leading to many important discoveries. • In 1905, Albert Einstein said that mass and energy can be converted into each other. • He showed that if matter is destroyed, energy is created, and if energy is destroyed mass is created. • E = MC2 ΔE = ΔKE+ΔPE

  39. Conservation of Energy Roller coasters work because of the energy that is built into the system. Initially, the cars are pulled mechanically up the tallest hill, giving them a great deal of potential energy. From that point, the conversion between potential and kinetic energy powers the cars throughout the entire ride.

  40. Pause for a Cause • A diver of mass m drops from a board 10.0 m above the water’s surface. Neglect air resistance. • a) Determine his speed 5.00 m above the water’s surface. • b) Determine speed at impact.

  41. Pause for a Cause • a) Determine his speed 5.00 m above the water’s surface.

  42. Pause for a Cause • a) Determine his speed 5.00 m above the water’s surface.

  43. Hooke’s Law F = -kx The force needed to stretch or compress a spring some distance is proportional to that distance.

  44. Springs: Elastic Potential Energy • Springs are found in all kinds of machines. • Watches • Pencils • Cars • Trains • Spring force is a conservative force • Ex: • Exception Work-energy theory Wnc= ΔKE+ΔPEg+PEs

  45. Hooke’s Law F- is the restoring force because the spring always exerts a force opposite of the displacement • Elastic potential energy • Fs = -kx • Fs-force of spring • k-spring constant • x-distance • Experiments have found that doubling the displacement requires double the force

  46. Pause for a Cause • The spring with a k-value of 163.5 N/m, is compressed after a force of 450 N is applied. • Determine the distance the spring was compressed

  47. Pause for a Cause • The spring with a k-value of 163.5 N/m, is compressed after a 50.0 kg box with velocity 18 m/s in 2 seconds. • Determine the distance the spring was compressed

  48. Work Done by a Spring • Work done by a spring • Work-energy Theorem

  49. Pause for a Cause • A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring. 3.3 J Xi = 2.45 m stretched Xf = 3.57 m

  50. Pause for a Cause • A block with a mass of 5.00 kg is attached to a horizontal spring with a spring constant k = 4.00 x 102 N/m. The surface the block rest upon is frictionless. If the block is pulled out to xi = 0.0500 m and released • A) Find the speed when it reaches equilibrium

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