Work,Energy and Power

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  • P = 2195.2 W
  • Work,Energy and Power

    1. 1. Work, energy and power<br />
    2. 2. The Ninja, a roller coaster at Six Flags over Georgia, has a height of 122 ft and a speed of 52 Mph. The potential energy due to its height changes into kinetic energy of motion.<br />
    3. 3. WORK<br />Work is done by force when there is a force applied on the body and the body must move with a displacement in line with the force applied.<br />𝐹<br />Β <br />𝐹<br />Β <br />𝐹<br />Β <br />πœƒ<br />Β <br />πœƒ<br />Β <br />πœƒ<br />Β <br />𝐹<br />Β <br />βˆ†π‘ <br />Β <br />πœƒ= angle bet. 𝐹and βˆ†π‘ <br />𝐹|| = component of 𝐹 parallel with βˆ†π‘ <br />Β <br />πœƒ<br />Β <br />βˆ†π‘ <br />Β <br />𝐹||<br />Β <br />π‘Š=𝐹||βˆ†π‘ =πΉβˆ†π‘ cosπœƒ<br />Β <br />Work done by constant force<br />
    4. 4. 𝑾 canΒ beΒ Β Β +                                 𝑖𝑓𝑓 𝐹βˆ₯βˆ†π‘ Β (0π‘œβ‰€πœƒ<90π‘œ)βˆ’Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β π‘–π‘“π‘“Β πΉβˆ₯βˆ†π‘ Β (90π‘œ<πœƒβ‰€180π‘œ)πŸŽΒ Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β Β π‘–π‘“π‘“Β πΉΒ βŠ₯βˆ†π‘ Β (πœƒ=90π‘œ)<br />Β <br />Units of work: <br /> joule, J (1 J = 1 N-m)<br />erg (1 erg = 1 dyne-cm)<br />ft-lb<br />
    5. 5. Example 01<br />Demi horizontally pushes the 200-N crate in a rough horizontal plane with a constant force of 90 N to continuously move it in uniform motion at a distance of 100 m. What is the total work done on the crate?<br />
    6. 6. energy<br />Energyis anything that can be converted into work; i.e., anything that can exert a force through a distance. <br />Energy is the capability for doing work.<br />Unit of energy is the same to the unit of work.<br />Other units used:<br />calorie<br />British Thermal Unit (Btu)<br />kilowatt-hour<br />
    7. 7. Kinds of Mechanical Energy<br />Kinetic Energy, K – β€œspeed”<br />Potential Energy, U – β€œposition” or β€œcondition”<br />a. Gravitational PE, Ug<br />b. Elastic PE<br />c. Electric PE<br />Transit Energies: KE and Heat<br />”<br />
    8. 8. Work done and Kinetic Energy<br />𝑣<br />Β <br />π‘£π‘œ<br />Β <br />𝑃<br />Β <br />𝑃<br />Β <br />βˆ†π‘ <br />Β <br />π‘Ž=𝑣2βˆ’π‘£π‘œ22βˆ†π‘ <br />Β <br />𝐹||=π‘šπ‘£2βˆ’π‘£π‘œ22βˆ†π‘ <br />Β <br />𝐹=π‘šπ‘Ž<br />Β <br />𝐹||βˆ†π‘ =12π‘šπ‘£2βˆ’12π‘šπ‘£π‘œ2<br />Β <br />𝐾=12π‘šπ‘£2<br />Β <br />Kinetic energy<br />βˆ΄π‘Š=πΎβˆ’πΎπ‘œ=βˆ†πΎ<br />Β <br />Work-Energy Theorem<br />Work done on the body by resultant forces is its change in kinetic energy<br />
    9. 9. Work done by gravity (weight) and gravitational potential energy<br />π‘Šπ‘€=π‘€βˆ†π‘ cosπœƒ<br />Β <br />𝑀<br />Β <br />π‘Šπ‘€=π‘šπ‘”π‘¦βˆ’π‘¦π‘œcos180<br />Β <br />βˆ†π‘ <br />Β <br />𝑦<br />Β <br />π‘Šπ‘€=π‘šπ‘”π‘¦π‘œβˆ’π‘šπ‘”π‘¦<br />Β <br />𝑀<br />Β <br />π‘¦π‘œ<br />Β <br />π‘ˆπ‘”=π‘šπ‘”π‘¦<br />Β <br />Gravitational potential energy<br />βˆ΄π‘Š=π‘ˆπ‘œβˆ’π‘ˆ=βˆ’βˆ†π‘ˆ<br />Β <br />Work done on the body is its negative change in potential energy<br />
    10. 10. Review first:<br />Work<br />π‘Š=𝐹||βˆ†π‘ =πΉβˆ†π‘ cosπœƒ<br />Β <br />𝐾=12π‘šπ‘£2<br />Β <br />Kinetic Energy<br />Gravitational Potential Energy<br />π‘ˆπ‘”=π‘šπ‘”π‘¦<br />Β <br />Work-Energy Theorem<br />π‘Š=βˆ†πΎ<br />Β <br />
    11. 11. since<br />π‘Š1+π‘Š2+…=βˆ†πΎ<br />Β <br />π‘Š=βˆ†πΎ<br />Β <br />π‘Š1=βˆ’βˆ†π‘ˆ<br />Β <br />π‘Š2+ …=Β π‘Šπ‘œπ‘‘hπ‘’π‘Ÿ=workΒ doneΒ byΒ otherΒ forces<br />Β <br />βˆ΄Β Β Β Β Β Β Β Β Β βˆ’βˆ†π‘ˆ+π‘Šπ‘œπ‘‘hπ‘’π‘Ÿ=βˆ†πΎ<br />Β <br />π‘ˆπ‘œβˆ’π‘ˆ+π‘Šπ‘œπ‘‘hπ‘’π‘Ÿ=πΎβˆ’πΎπ‘œ<br />Β <br />Law of Conservation of Energy<br />πΎπ‘œ+π‘ˆπ‘œ+π‘Šπ‘œπ‘‘hπ‘’π‘Ÿ=𝐾+π‘ˆ<br />Β <br />Initial energy = final energy<br />
    12. 12. Examples: Use energy methods to solve all problems<br />A bus slams on brakes to avoid an accident. The thread marks of the tires is 25 m long. If πœ‡π‘˜=0.70, what was the speed of the bus before applying brakes?<br />A 1.50-kg book is dropped from a height of 15.0 m from the ground. Find its potential and kinetic energy when it is 6.0 m from the ground.<br />A small rock with a mass of 0.20kg is released from rest at point A, which is at the top edge of a large hemispherical bowl with radius R = 0.80m. Assume that the size of the rock is small in comparison to the radius of the bowl, so the rock can be treated as particle, the work done by the friction when it moves from point A to point B at the bottom of the bowl is -0.22J. What is the speed of the rock when it reaches point B?<br />Β <br />
    13. 13. Power<br />Power is defined as the rate at which work is done.<br />𝑷=βˆ†π‘Ύβˆ†π’•<br />Β <br />Power<br />Units of Power:<br /> watt, W 1Β W=1Β J/s<br /> erg/s<br />foot=pound per second (ft-lb/s)<br />horsepower 1Β hp=746Β W<br />Β <br />
    14. 14. Power and velocity<br />Recall average speed or constant velocity: 𝑣=𝑑𝑑<br />Β <br />So that 𝑑=𝑣𝑑<br />Β <br />Since π‘Š=𝐹𝑑 and 𝑃=π‘Šπ‘‘<br />Β <br />𝑃=𝐹𝑑𝑑=𝐹𝑣𝑑𝑑<br />Β <br />Power at constant velocity<br />𝑃=𝐹𝑣<br />Β <br />
    15. 15. Example of Power<br />What power is consumed in lifting a 70.0-kgrobber 1.6m in 0.50 s?<br />𝑃=π‘Šβˆ†π‘‘<br />Β <br />𝑃=𝐿𝑦𝑑<br />Β <br />𝑃=π‘šπ‘”π‘¦π‘‘<br />Β <br />𝑃=(70.0Β kg)(9.8Β ms2)(1.6Β m)Β 0.50Β s<br />Β <br />P= 2200 W=2.2 kW<br />
    16. 16. MORE PROBLEMS<br />Use energy methods to solve all problems<br />1. Tarzan swings on a 30.0-m-long vine initially inclined at an angle of 37.0o with the vertical. What is his speed at the bottom of the swing (a) if he starts from rest? (b) if he pushes off with a speed of 4.00m/s? hint: the work done by tension is zero.<br />2. A 45.0-kg block of wood initially at rest is pulled by a cord from the bottom of a 27.0o inclined plane. The tension of the cord is 310 N parallel to the plane. After travelling a distance of 2.0 m , the speed of the block is 5.0 m/s. (a) what is the work done by friction? (b) what is the coefficient of friction?<br />3. A 750-N box is pulled in a rough horizontal plane by a motor driven cable. The coefficient of kinetic friction between the box and the plane is 0.40. (a) How much work is required to pull it 60 m at a constant speed of 2.0 m/s? (b) What power must the motor have to perform this task?<br />

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