How large a force is necessary to stretch a 2.0 mm radius steel wire (Y = 2.0 *10¹¹ N/m²) by 2.0%? A) 5.0 * 10⁴ N B) 2.5 * 10⁴ N C) 2.5 *10³ N D) 1.3 * 10⁴ N

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The stress on the wire is:$$\sigma = Y \epsilon = (2.0 	imes 10^{11} N/m^2)(0.02) = 4.0 	imes 10^9 N/m^2$$The force on the wire is:$$F = \sigma A = (4.0 	imes 10^9 N/m^2)(\pi (2.0 	imes 10^{-3} m)^2) = 5.0 	imes 10^4 N$$

How Large a Force Is Necessary to Stretch a 2