**Understanding the Work Done to Stretch a Spring**The graph below illustrates the relationship between the force exerted by a spring and the distance \( x \) that the spring is stretched. This is a common physics problem that involves Hooke's Law, which states that the force \( F \) exerted by a spring is directly proportional to its extension \( x \), described by \( F = kx \), where \( k \) is the spring constant.**Questions:**1. How much work is needed to stretch the spring a distance of 5.0 cm, starting with it unstretched?2. How much work is needed to stretch the spring from \( x = 2.0 \) cm to \( x = 7.0 \) cm?**Graph Description:**- The y-axis represents the force \( F \) in Newtons (N). - The force ranges from 0 N to 350 N, with increments of 50 N.- The x-axis represents the displacement \( x \) in centimeters (cm). - The displacement ranges from 0 cm to 8 cm, with increments of 1 cm.- The graph is a straight line passing through the origin (0,0), which indicates a linear relationship between force and displacement. This linear trend confirms Hooke's Law, \( F = kx \).To find the work done (\( W \)) to stretch the spring, we use the formula for the work done in stretching a linear spring:\[ W = \frac{1}{2} k x^2 \]**Solving the Questions:**1. **For stretching the spring from 0 cm to 5.0 cm:** - Determine the spring constant \( k \): By reading from the graph, at \( x = 5.0 \) cm, \( F = 200 \) N. Using \( F = kx \): \[ 200 \, \text{N} = k \cdot 5.0 \, \text{cm} \] Convert 5.0 cm to meters: \[ 5.0 \, \text{cm} = 0.05 \, \text{m} \] Then: \[ k = \frac{200 \, \text{N}}{0.05 \, \text{m

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Description: **Understanding the Work Done to Stretch a Spring**The graph below illustrates the relationship between the force exerted by a spring and the distance \( x \) that the spring is stretched. This is a common physics problem that involves Hooke's Law,

We need to calculate the work done in stretching the spring by the given amounts in parts a and b.

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The graph in the figure below shows the magnitude of the force ex- erted by a given spring as a function of the distance x the spring is stretched. How much work is needed to stretch this spring: (a) a distance of 5.0 cm, starting with it unstretched, and (b) from x = = 2.0 cm to x = 7.0 cm? F (N) 350 300 250 200 150

The graph in the figure below shows the magnitude of the force ex- erted by a given spring as a function of the distance x the spring is stretched. How much work is needed to stretch this spring: (a) a distance of 5.0 cm, starting with it unstretched, and (b) from x = = 2.0 cm to x = 7.0 cm? F (N) 350 300 250 200 150

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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