question_answer 43)

                  A truck is pulling a car out of a ditch by means of a steel cable that is 9.1 m long and has a radius of 5 mm. When the car just begins to move, the tension in the cable is 800 N. How much has a cube stretched? (Young?s modulus for steel is \[2\times {{10}^{11}}N{{m}^{2}}\].)                               

Answer:

                  \[Y=\,\frac{FL}{\pi {{r}^{2}}\Delta L}\] \[\therefore \] \[\Delta L=\,\frac{FL}{\pi {{r}^{2}}Y}\]                 or \[\Delta L=\,\frac{800\,\times \,\,9.1}{3.14\,\times \,25\,\,\times \,{{10}^{-6}}\times \,2\times \,{{10}^{11}}}\]                 \[=4.64\times {{10}^{4}}m\]