Question

The length, L, that a spring is stretched varies directly as the amount of force, F, applied to the end of the spring. When a force of 10 pounds is applied to a spring, it stretches 3 inches. How much will the same spring stretch if the force is increased to 15 pounds?

A) 4.5 inches
B) 2 inches
C) 5 inches
D) 1.5 inches

Answer 1

When the force on a spring is increased from 10 pounds to 15 pounds, the spring stretches from 3 inches to 4.5 inches, maintaining a direct linear relationship between force and length stretched.

Step-by-step explanation:

The length, L, that a spring is stretched varies directly with the amount of force, F, applied. This means that as the force increases, the stretch of the spring also increases in a linear relationship. This concept can be modeled by the equation L = kF, where k is a constant of proportionality. Given that a force of 10 pounds stretches the spring 3 inches, we can calculate the constant k as k = L/F = 3 inches / 10 pounds.

We then determine the new length when the force is increased to 15 pounds using the constant k: L = kF = 3 inches/10 pounds × 15 pounds = 4.5 inches. Therefore, the correct answer is A) 4.5 inches.