## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 5 - Problems - Page 185: 15

#### Answer

(a) The safe radius of curvature is $885.5~m$ (b) The safe radius of curvature is $491.9~m$

#### Work Step by Step

(a) We can convert the speed from units of km/h to units of m/s: $750~km/h \times \frac{1000~m}{1~km} \times \frac{1~h}{3600~s} = 208.3~m/s$ We can find the safe radius of curvature when $a_c = 5.0~g$: $a_c = \frac{v^2}{r}$ $5.0~g = \frac{v^2}{r}$ $r = \frac{v^2}{5.0~g}$ $r = \frac{(208.3~m/s)^2}{(5.0)(9.80~m/s^2)}$ $r = 885.5~m$ The safe radius of curvature is $885.5~m$ (b) We can find the safe radius of curvature when $a_c = 9.0~g$: $a_c = \frac{v^2}{r}$ $9.0~g = \frac{v^2}{r}$ $r = \frac{v^2}{9.0~g}$ $r = \frac{(208.3~m/s)^2}{(9.0)(9.80~m/s^2)}$ $r = 885.5~m$ The safe radius of curvature is $491.9~m$

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