To solve the problem, we need to analyze the relationship between force and elongation in a spring, assuming Hooke's Law applies. Hooke's Law states that the force \( F \) applied to a spring is proportional to the elongation \( x \), represented by the equation \( F = kx \), where \( k \) is the spring constant.
Step 1: Understand the given data
For a force of 3 N, the elongation is \( a \). Thus, \( 3 = ka \). For a force of 2 N, the elongation is \( b \), giving \( 2 = kb \).
Step 2: Express \( a \) and \( b \) in terms of \( k \)
From \( 3 = ka \), we get \( a = \frac{3}{k} \). From \( 2 = kb \), we obtain \( b = \frac{2}{k} \).
Step 3: Calculate \( 2a - 3b \)
Substitute the values of \( a \) and \( b \): \( 2a = 2 \left(\frac{3}{k}\right) = \frac{6}{k} \) \( 3b = 3 \left(\frac{2}{k}\right) = \frac{6}{k} \)
