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The Work-Energy Theorem

The Work-Energy Theorem. Derivation: v f 2 =v i 2 +2ad Kinematics Equation mv f 2 =mv i 2 +2mad Dynamics equation (1/2)[mv f 2 =mv i 2+2mad] mad= ½ mv f 2 - ½ mv i 2 KE=kinetic energy = ½ mv 2 Kinetic Energy: The energy associated with the motion of a mass

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The Work-Energy Theorem

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  1. The Work-Energy Theorem Derivation: vf2=vi2+2ad Kinematics Equation mvf2=mvi2+2mad Dynamics equation (1/2)[mvf2=mvi2+2mad] mad= ½ mvf2- ½ mvi2 KE=kinetic energy = ½ mv2 Kinetic Energy: The energy associated with the motion of a mass The amount of capable work associated with the motion of a mass. Measured in Joules (J) KE is a scalar quantity.

  2. Kinetic Energy Considerations • A small mass moving at a high speed can have the same kinetic energy (do the same work) as a large mass that travels slowly. • You have two equivalent masses, mass A and B. Suppose you double the mass of A and double the speed of mass B. Which mass now has more KE? • Why? • A car traveling at a certain speed stops after travel a distance, d, after the brakes are applied. Suppose that the speed of the car is double, by what factor does the distance to stop change provided that the braking for is the same as the first situation.

  3. Things for Thought • A 2 g bumblebee moving at 2 m/s has a kinetic energy of 4x10-3 J which means it is capable of doing 4x10-3 J of work • A comet with a mass of 7.9x1011 kg traveling at 25,000 m/s has a kinetic energy or capable of doing 2.5x1020J of work. The most powerful atomic bomb has an energy yield of 5x1015 J, thus this comet can do 5000 times more work.

  4. Various Forms of the Work-Energy Theorem mad= ½ mvf2- ½ mvi2 (Fnet)d=KEf-KEi KEf=final kinetic energy, KEi=initial kinetic energy Wnet=KEf – KEi Wnet=ΔKE • The net work accomplished on mass causes a change in its kinetic energy. • The work-energy theorem is a cause and effect relationship. The net work on a mass causes a change in its kinetic energy. • Positive Net Work – increases the speed of a mass causing a positive change in kinetic energy. • Net Negative Work – decreases the speed of a mass causing a negative change in kinetic energy.

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