# lecture20 - Work and Kinetic Energy Work by a variable...

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1 Physics 1D03 Work and Kinetic Energy Work by a variable force Kinetic Energy and the Work-Energy Theorem Serway 7.4, 7.5 Suggested Problems : Chapter 7, problems 15, 17, 21, 31, 35 Physics 1D03 Work is the area under a graph of force vs. distance: dx F W x x f i = i x f x Split displacement into short steps Δ x over which F is nearly constant. .. F(x) x i x f x F(x) x Take the limit as x 0 and the number of steps → ∞ x F W Δ We get the total work by adding up the work done in all the small steps. As we let x become small, this becomes the area under the curve, and the sum becomes an integral.

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2 Physics 1D03 In 1D (motion along the x-axis): dx F W x x f i = Another way to look at it: Suppose W(x) is the total work done in moving a particle to position x. The extra work to move it an additional small distance Δ x is, approximately, W F(x) x. Rearrange to get x W x F Δ Δ ) ( In the limit as x goes to zero, dx dW x F = ) ( Physics 1D03 Example: an ideal spring. Hooke’s Law: The tension in a spring is proportional to the distance stretched. or,
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lecture20 - Work and Kinetic Energy Work by a variable...

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