The length a spring stretches is directly proportional to the force applied. If a force of 8 pounds stretches a spring 10 inches, how much force is necessary to stretch the same spring 9 inches?

x = kF

x/F is constant. You want F such that

9/F = 10/8

10

The length a spring stretches is directly proportional to the force applied. If a force of

2
pounds stretches a spring
4
inches, how much force is necessary to stretch the same spring
3
Inches?

To solve this problem, we can use the concept of direct proportionality. Direct proportionality states that if one quantity is directly proportional to another, their ratio remains constant.

In this case, the length a spring stretches is directly proportional to the force applied. We can express this relationship as:

(length of stretch) / (force) = constant

We are given that a force of 8 pounds stretches the spring 10 inches. Let's calculate the constant of proportionality:

constant = (length of stretch) / (force) = 10 inches / 8 pounds

Now, we can use this constant to find the force necessary to stretch the same spring 9 inches:

force = (length of stretch) / (constant) = 9 inches / (10 inches / 8 pounds)

Simplifying the expression:

force = 9 inches * (8 pounds / 10 inches) = 7.2 pounds

Therefore, the force necessary to stretch the same spring 9 inches is 7.2 pounds.