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Calculating Work

Calculating Work. The Joule. Work is force acting over a distance, and has units equal to units of force times units of distance. With 1-dimensional constant force and distance, W = F D x The unit of work is the joule (J) = 1 N m. Constant Force.

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Calculating Work

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  1. Calculating Work

  2. The Joule • Work is force acting over a distance, and has units equal to units of force times units of distance. • With 1-dimensional constant force and distance, W = FDx • The unit of work is the joule (J) = 1 N m.

  3. Constant Force • Lifting an object requires a constant force equal to gravity, F = mg. • The work done by the lifter is W = FDx = mgh. • The work done by gravity is W = - FDx = -mgh. mg x = h -mg mg -mg

  4. Using the Scalar Product • A man is letting a 300 kg piano slide 4 m at constant velocity down a 30° incline while exerting a 400 N force on the horizontal. What work does he do? • The component of the force is (400 N)(cos 30) = -350 N • Negative since it is opposite the displacement • The work is (-350 N)(4 m) = -1400 N m = -1400 J Dx F

  5. Variable Force • The force applied to a spring increases as the distance increases. • The work must be calculated over each separate interval. • The work increases over a small interval as the force increases. F Dx

  6. Area under a Curve • Separate the total distance into steps Dx. • The product within a small step is the area of a rectangle FDx. • The total equals the area between the curve and the x axis. F Dx

  7. Work on a Spring • For the spring force the force makes a straight line. • The area under the line is the area of a triangle. F=kx x

  8. Integral Form of Work • The work can be found by taking the area under any force curve. • This technique in calculus is the integral. F x next

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