Track / Stage 4 / 303 of 340 #563 of 1964

Problem 563

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

Example 2. How much work is required to stretch a spring by $0.06 m$ , if a force of 1 N stretches it by 0.01 m?

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

Solution. According to Hooke's law, the force $X$ stretching the spring by $x \mu$ is $X=k x$ , where $k$ is the proportionality coefficient. Assuming $x=0.01$ m and $X=1$ N, we get $k=100$ , therefore, $X=k x=100 x$ . The sought work is determined by the formula (5.24):

$A=\int_{0}^{0.06} 100 x d x=\left.50 x^{2}\right|_{0} ^{0.06}=0.18(\partial \varkappa)$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.