Question

what is the total number of centimeters that a force of 60 newtons will stretch the same spring?
hookes law states that the force needed to stretch a spring varies directly with the length the spring is stretched. a force of 20 newtons will stretch a spring 5 centimeters. what is the total number of centimeters that a force of 60 newtons will stretch the same spring?
○15
○20
○100
○240

Explanation:

Step1: Define Direct Variation

For direct variation, \( F = kx \), where \( F \) is force, \( x \) is stretch length, and \( k \) is constant. Given \( F = 20 \, \text{N} \), \( x = 5 \, \text{cm} \), find \( k \).
\( 20 = k \times 5 \) → \( k = \frac{20}{5} = 4 \).

Step2: Find Stretch for \( F = 60 \, \text{N} \)

Use \( F = kx \) with \( k = 4 \), \( F = 60 \).
\( 60 = 4x \) → \( x = \frac{60}{4} = 15 \).

Answer:

15 (corresponding to the option "15")