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Work and Energy

Work and Energy. Work. Work is said to be done when an applied force, f moves an object thru a distance, d. W = f x d In the metric system, the unit of force is in Newton (N), unit of distance is in meters (m), and the unit of work is in Joules (J). Work. When force is applied

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Work and Energy

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  1. Work and Energy

  2. Work Work is said to be done when an applied force, f moves an object thru a distance, d. W = f x d In the metric system, the unit of force is in Newton (N), unit of distance is in meters (m), and the unit of work is in Joules (J).

  3. Work When force is applied at an angle, θ, then only the cosine component of the force does work. Then W = f d cos θ Here again the unit of Work is in Joules (J).

  4. Work due to non-constant force Work done by a non-constant force can be calculated by finding the area under a Force-displacement graph. Here the area is a triangle. So, W=(1/2)F.d

  5. Gravitational Potential Energy Work done by gravity (loss of height) and against gravity (gain of height) is called GPE. { w = fd, f = ma or f =mg (if gravity applies the force); so w = mgd or w = mgh) Gravitational Potential Energy = mgh Unit of m is kilograms (Kg) “g” is acceleration due to gravity and on earth it is 9.8 or 10m/s2. “h” is the height and is in meters (m) Unit of GPE in metric system is Joules.

  6. Kinetic Energy It is the energy of motion F=ma F=m(Vf-Vi)/t F=m (½)vavg/t W=F x d W= m (½)vavg(d/t) = (½)mv2 KE= (½) mv2 In the metric system, the mass is in kilograms (kg), the velocity is in meters/second (m/s) and KE is in Joules (J)

  7. Work to KE Work has to be done to make an object move. Work = KE F d = (½) mv2 This is conversion of work to KE. Example: Throwing a ball. You have to apply a force through a distance on a ball to make it move.

  8. Work to GPE Work has to be done to lift or drop an object. Work = GPE Fd = mgh This is conversion of work to GPE. Example: Lifting or dropping a ball. You have to apply a force through a height (distance) on a ball to lift a ball. Gravity applies a force through a height (distance) on a ball dropped from a height.

  9. Units of work and/or Energy • Unit of work or energy in Metric System is in Joules. • Some times the unit of Energy can also be in KWh (Kilo-Watt-hour). • Most Energy Companies use KWh. But here they mean electrical energy.

  10. Conservation of energy (COE) COE states that energy can transform from one form to another, but cannot be created or destroyed. Let us take the example of a skate boarder or the Bowling ball, or the Happy ball-Sad ball Lab or the Toy car efficiency Lab. TMEi = TMEf TME stand for Total Mechanical Energy. If we take the initial, “i” at the left extreme end and final, “f” in the middle, then we using TMEi = TMEf We get PE = KE or mgh = (½) mv2

  11. GPE = KE We can solve this problem, using _________. m=2kg 30m Find the velocity of the ball at the bottom of the hill. Answer: _______ 24 m/s

  12. GPE = KE We can solve a similar problem using _______, even without knowing the mass of the object. Because _______ cancels out on both sides. Find speed of the ball at the bottom of the hill. Answer: ___________. mass 50m 31.7 m/s

  13. Similarly we can solve this by using this relationship __________________. 10m/s Find the maximum height this ball can reach. Answer: _______. KE = GPE 5 m

  14. Total Energy Total Mechanical Energy Total non Mechanical Energy Kinetic Energy Potential Energy Gravitational Elastic Kinetic Energy Potential Energy Energy loss to friction Gravitational Elastic

  15. Conservation of Energy, COE • The total Mechanical Energy (TME) in a conservative system is conserved. TMEi = TMEf [PE + KE]before= [PE + KE]after • The TME in a non-conservative system is not conserved (cannot be transformed). Some energy is lost as Thermal Energy due to friction. [PE + KE]before= [PE + KE + Frictional losses]after

  16. Problem 1 – Roller Coaster: 3m/s 60m 40m 15m • Determine the velocity of a coaster at the top of the loop. Assume frictionless track. • Using: • Answer: ____________ PEi + KEi = PEf + KEf 20 m/s

  17. Problem 2 – Pole Vault 8m/s Determine the initial ground speed of this pole vaulter when she passes over the 10m high bar at the speed of 8m/s. Using: , we get __________ KEi = PEf + KEf 16.2m/s

  18. Problem 3 – Non conservative force 30m A 40kg child sleds down the hill. Find his velocity at the bottom. Assume frictionless hill. If he hits packed snow and slows to speed of 10m/s, find energy lost to friction.

  19. Power and its unit Power = Work or Energy/Time We have just learned that work done can be converted to KE or PE. So Power = Work/time Or Power = KE/Time Or Power = PE/Time Or Power = Total Energy/Time Metric unit of Power is Watts. 1 Calories = 1kcalorie = 4186J Horse power is also a unit of power and 1Hp = 746 Watts

  20. Problem – Roller Coaster: 3m/s 60m 40m 15m • Find the power of the motor that can lift a 500kg car to the top of the first hill in 10 sec. • (Hint – remember that at the top of the first hill, the car has some speed also.)

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