Question

a box that has a weight of 40 n is hung from a spring. the spring constant of the spring is 400 n/m. how many centimeters will the spring stretch? 10 cm, 1 cm, 100 cm, 0.1 cm

Explanation:

Step1: Recall Hooke's Law

Hooke's Law states that the force \( F \) exerted by a spring is \( F = kx \), where \( k \) is the spring constant and \( x \) is the displacement (stretch or compression). Here, the weight of the box is the force \( F \), so \( F = 40\ N \) and \( k = 400\ N/m \). We need to solve for \( x \). Rearranging Hooke's Law gives \( x=\frac{F}{k} \).

Step2: Calculate the stretch in meters

Substitute \( F = 40\ N \) and \( k = 400\ N/m \) into the formula: \( x=\frac{40}{400}=0.1\ m \).

Step3: Convert meters to centimeters

Since \( 1\ m = 100\ cm \), multiply the length in meters by 100: \( 0.1\ m\times100 = 10\ cm \).

Answer:

10 cm