Chapter 13a

# Chapter 13a - Chapter 13A Review of Hooke's Law For elastic...

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Chapter 13A 1 Review of Hooke’s Law For elastic tensile deformations: F A = Y L L 0 F = YA L 0 L F = kx ( x = ∆ L ) For a given object, Y , A , and L 0 will remain constant

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Chapter 13A 2 Hooke’s Law Applied to Springs The force needed to stretch or compress a spring is: x = distance spring is stretched or compressed k = spring constant, or force constant The constant k defines the spring’s stiffness Units for k : (N/m) F = kx
Chapter 13A 3 Restoring Force Newton’s third law tells us that the spring will exert an equal but opposite restoring force : The force needed to stretch or compress a spring is: F = kx In both cases F is proportional to x , the spring’s displacement from its equilibrium position. F = - kx F and x are in the same direction. F and x are in opposite directions.

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Chapter 13A 4 Elastic Potential Energy When we stretch a spring we do work on it: W = F x F = kx where Between x i and x f the average force is F = 1 2 k x i + x f ( 29 and the distance traveled is x = x f - x i
5 Elastic Potential Energy for the work done on the spring. This gives: W = 1 2 kx f 2 - 1 2 kx i 2 The quantity is elastic potential energy . When we do positive work on a spring we are putting

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Chapter 13a - Chapter 13A Review of Hooke's Law For elastic...

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