QUESTION 2 FIGURE 2.2 FIGURE \( 2.2 \) shows one end of a horizontal spring \( \left(\mathrm{k}-80.0 \mathrm{~N} \mathrm{~m}^{-1}\right) \) is held fixed while an external force is applied to the free end, stretching in slowly frem \( x=0 \mathrm{to} x=4.00 \mathrm{~cm} \). (a) Calculate the work done by the appliod foree on the spring. (b) Calculae the aditional wonk done in stretching the spring from \( x=4.00 \mathrm{~cm} 10 x=7.00 \mathrm{~cm} \). [ \( [5 \) marks Page 4 of 9
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In Problem 4 (a) Find the work done in stretching the spring $0.2 \mathrm{~m}$. (b) Find the work done in stretching the spring from a length of $1 \mathrm{~m}$ to a length of $1.1 \mathrm{~m}$.
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In Figure $10-20$, the magnitude of the force necessary to stretch a spring is plotted against the distance the spring is stretched. a. Calculate the slope of the graph, $k,$ and show that $F=k d$, where $k=25 \mathrm{N} / \mathrm{m}$ b. Find the amount of work done in stretching the spring from 0.00 $\mathrm{m}$ to $0.20 \mathrm{m}$ by calculating the area under the graph from 0.00 m to 0.20 m. c. Show that the answer to part b can be calculated using the formula $W=\frac{1}{2} k d^{2},$ where $W$ is the work, $k=25 \mathrm{N} / \mathrm{m}$ (the slope of the graph), and $d$ is the distance the spring is stretched $(0.20 \mathrm{m})$
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$\bullet$ $\bullet$ The graph in the accompanying figure shows the magni- tude of the force exerted 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 $5.0 \mathrm{cm},$ starting with it unstretched, and (b) from $x=2.0 \mathrm{cm}$ to $x=7.0 \mathrm{cm} ?$
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