How large a force is necessary to stretch a 2.0-mm-diameter steel wire (Y = 2.0 ´ 10¹¹ N/m²)by 1.0%? A)3.1 ´ 10³ N B)6.3 ´ 10³ N C)9.4 ´ 10³ N D)1.3 ´ 10⁴ N

Question

Quizplus · Accepted Answer

The formula for calculating the force required to stretch a wire is:

F = (π/4) * Y * (d^2) * ε

where F is the force, Y is the Young's modulus of the wire, d is the diameter of the wire, and ε is the strain (or percentage of stretch).

Substituting the values given in the problem, we get:

F = (π/4) * (2.0 × 10^11 N/m^2) * (2.0 × 10^-3 m)^2 * 0.01

F = 6.28 × 10^7 N

Round off to two significant figures, the answer is B: 6.3 × 10^13 N.

How Large a Force Is Necessary to Stretch a 2