## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

We can write an expression for the initial speed which is 150 m/s: $v_1 = \sqrt{\frac{T_1}{\mu}}$ We can write an expression for the final speed which is 180 m/s: $v_2 = \sqrt{\frac{T_2}{\mu}}$ We can divide the second equation by the first equation. $\frac{v_2}{v_1} = \frac{\sqrt{\frac{T_2}{\mu}}}{\sqrt{\frac{T_1}{\mu}}}$ $\frac{\sqrt{T_2}}{\sqrt{T_1}} = \frac{v_2}{v_1}$ $\sqrt{T_2} = \sqrt{T_1}~\frac{v_2}{v_1}$ $T_2 = T_1~(\frac{v_2}{v_1})^2$ $T_2 = (75.0~N)~(\frac{180~m/s}{150~m/s})^2$ $T_2 = 108~N$ A tension of 108 N will give a speed of 180 m/s.