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lecture 11 - Lecture 11 Springs Hooke's law Work by...

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1 Lecture 11 Springs Hooke’s law Work by nonconstant forces Power
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2 Springs If I pull the spring to the right, the spring pulls to the left on me. Experiments with some springs show that F applied spring stretch so that F = –k x (Hooke’s law).
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3 ( 29 ( 29 2 i 2 f 2 spring 2 1 2 1 2 1 ˆ ˆ f f kx kx kx dx kx d W x x x x i i + - = - = - = = x x r F The work done by a spring is The work done by the external agent to stretch the spring (at constant v) is ( 29 ( 29 2 i 2 f F 2 1 2 1 ˆ ˆ f kx kx dx kx d W x x i - = + = = x x r F
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4 What is the spring constant? In equilibrium, the FBD for the mass is F sm w em y x x mg k mg kx w F F y = = - = = - = 0 0 em sm k is a measure of spring stiffness
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5 Example: An ideal spring has k = 20.0 N/m. What is the amount of work done (by an external agent) to stretch the spring 0.40 m from its relaxed length? ( 29 ( 29 J 6 . 1 m 40 . 0 N/m 0 . 20 2 1 2 1 2 m 40 . 0 0 2 m 40 . 0 0 = = = = = kx Fdx d W r F
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6 How much additional work must be done to stretch the spring to 0.80 m?
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