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Work and Mechanical Energy

Work and Mechanical Energy. Formula and Transitions. Work. Formula: _______ , where θ is the angle between the force and the direction of motion: E.g. A box on a frictionless surface is pushed with a force of 13N for a distance of 3.5 m. How much work was done: W = . Work (cont.).

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Work and Mechanical Energy

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  1. Work and Mechanical Energy Formula and Transitions

  2. Work • Formula: _______, where θ is the angle between the force and the direction of motion: • E.g. A box on a frictionless surface is pushed with a force of 13N for a distance of 3.5 m. How much work was done: • W =

  3. Work (cont.) • A toboggan is being dragged as shown below. If the dude does 350J of work over what 12m, how much force did he apply? • W=Fdcosθ • F = • d = = 30°

  4. Gravitational Potential Energy • ΔEp = ___________ • Example: A 2.5kg book is given 45J more of potential energy by lifting it up from a chair to a book shelf. If the chair is 70cm high, how high is the book shelf? • ΔEp = mg Δh • Δh == ____m • Hbookshelf =

  5. Gravitational Potential Energy (cont.) • Continuing on from the previous example: • How much work was done to lift the book from the chair to the shelf? • Since the work done = __________ (work-energy theorem, isolated system), and all the energy change is gravitational potential, W = 45J • What force was applied to do this? W = Fdcosθ • F=

  6. Kinetic Energy • Ek = ______________ • A 1200kg car has 260kJ of kinetic energy. How fast is it going in km/h? • v =

  7. Kinetic energy (cont.) • The trucker applies the brakes which apply a frictional force of 1.50kN to slow the truck to 50 km/h. How much distance did this take to accomplish? • Using the work-energy theorem, the change in energy of the truck = work done: ΔEk= ________ • Ekf – Eki = Fdcosθ • ½mvf2 - ½mvi2 = Fdcosθ • ½m(vf2 - vi2) = Fdcosθ • d = • d = (note θ = 180 because the force (friction) is opposite to the direction of motion!) • d = 50km/hr = 13.8889m/s

  8. Elastic (spring) Potential Energy • Eps= ____where k is the spring constant in N/m and x = distance spring is compressed or stretched from its resting (equilibrium) position! • Example: if a spring requires15N of force to stretch it25 cm from equilibrium, what is its spring constant? • Since W = Epsin this case, then _________ = ½kx2 • x = d (the distance the force is applied is the stretching distance!) • So Fcosθ = • k =

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