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Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kr, for some constant k. The value of k (measured in force units per ur length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes a force of 17 N to compress a spring 0.3 m from the equilibrium position. Find the force function, F(x), for the spring described. F(z) = Part 2. Setup the integral that will give the work required to stretch the spring 0.6 m from the equilibrium position. W =

Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kr, for some constant k. The value of k (measured in force units per ur length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes a force of 17 N to compress a spring 0.3 m from the equilibrium position. Find the force function, F(x), for the spring described. F(z) = Part 2. Setup the integral that will give the work required to stretch the spring 0.6 m from the equilibrium position. W =

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.10: Modeling Variation
Problem 35E
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Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kr, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes a force of 17 N to compress a spring 0.3 m from the equilibrium position. Find the force function, F(x), for the spring described. F(x) = Part 2. Setup the integral that will give the work required to stretch the spring 0.6 m from the equilibrium position. W = Part 3. Calculate the work done by the force described above. W = Note: enter your answer using values correct to three decimal places.
Transcribed Image Text:Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kr, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes a force of 17 N to compress a spring 0.3 m from the equilibrium position. Find the force function, F(x), for the spring described. F(x) = Part 2. Setup the integral that will give the work required to stretch the spring 0.6 m from the equilibrium position. W = Part 3. Calculate the work done by the force described above. W = Note: enter your answer using values correct to three decimal places.
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.

a force of 17 N, stretches a spring 0.3 m from the equilibrium position.

so x=0.3 and F=13

from Hooke's law, spring constant k is

F=kx

17=k\cdot 0.3

k=\frac{17}{0.3}

k=\frac{170}{3}

.

F(x)=kx

substitute the value of k

{\color{Red} F(x)=\frac{170}{3}x}

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