Question
A Review problem. A wire of length $L,$ Young's modulus $Y,$ and cross-sectional area $A$ is stretched elastically by an amount $\Delta L$ . By Hooke's law, the restoring force is $-k \Delta L .$ (a) Show that $k=Y A / L .$ (b) Show that the work done in stretching the wire by an amount $\Delta L$ is$$W=\frac{1}{2} Y A \frac{(\Delta L)^{2}}{L}$$
Step 1
Step 1: We know that Young's modulus is defined as $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$, where $F$ is the force applied, $A$ is the cross-sectional area, $L$ is the initial length, and $\Delta L$ is the change in length. Show more…
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Review. A wire of length $L,$ Young's modulus $Y,$ and cross-sectional area $A$ is stretched elastically by an amount AL. By Hooke's law, the restoring force is $-k \Delta L .$ (a) Show that $k=Y A / L .$ (b) Show that the work done in stretching the wire by an amount $\Delta L$ is $W=\frac{1}{2} Y A(\Delta L)^{2} / L$.
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A wire of length $L,$ Young's modulus $Y$, and cross-sectional area $A$ is stretched elastically by an amount A $L$. By Hooke's law, the restoring force is $-k \Delta L$. (a) Show that $k=Y A / L$. (b) Show that the work done in stretching the wire by an amount $\Delta L$ is $W=\frac{1}{2} Y A(\Delta L)^{2} / L$.
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