Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 6 - Work and Energy - Problems - Page 166: 27



Work Step by Step

Tension force provides the centripetal force here. Before the guideline is pulled in, we have $T_i=\frac{mv_i^2}{r_i}$ After the guideline is pulled in, we have $T_f=\frac{mv_f^2}{r_f}$ From the information given, $T_f=4T_i$, so $$\frac{mv_f^2}{r_f}=\frac{4mv_i^2}{r_i}$$ $$\frac{v_f^2}{r_f}=\frac{4v_i^2}{r_i}$$ $$v_f=\sqrt{\frac{4r_fv_i^2}{r_i}}$$ We have $v_i=22m/s$, $r_i=16m$ and $r_f=14m$ $$v_f=41.16m/s$$ From the work-energy theorem, $$W=\frac{1}{2}m(v_f^2-v_i^2)$$ We know $m=0.9kg$, so $$W=544.6J$$
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