a 12 - pound weight attached to a spring stretches the spring by 2 inches. how many inches will the spring…

a 12 - pound weight attached to a spring stretches the spring by 2 inches. how many inches will the spring stretch if the 12 - pound weight is replaced with an 18 - pound weight?\na 2\nb 3\nc 4\nd 6

a 12 - pound weight attached to a spring stretches the spring by 2 inches. how many inches will the spring stretch if the 12 - pound weight is replaced with an 18 - pound weight?\na 2\nb 3\nc 4\nd 6

Answer

Explanation:

Step1: Find the spring - constant ratio

Since the force and the stretch of a spring are proportional (Hooke's law $F = kx$), and the ratio of forces is equal to the ratio of stretches. Let $F_1 = 12$ pounds, $x_1=2$ inches, $F_2 = 18$ pounds, and $x_2$ be the unknown stretch. The proportion is $\frac{F_1}{x_1}=\frac{F_2}{x_2}$.

Step2: Solve for $x_2$

Cross - multiply the proportion $\frac{12}{2}=\frac{18}{x_2}$ to get $12x_2=18\times2$. Then $12x_2 = 36$, and $x_2=\frac{36}{12}=3$ inches.

Answer:

B. 3