The length a spring stretches is directly proportional to the force applied. If a force of x pounds stretches a spring h inches, how much force is necessary to stretch the same spring m inches? (Assume x = 7, h = 4, and m = 15.)
7/4 as f/15 therefore 4 times 3.75 = 15
then 7 times 3.75 = 26.25
Answer: 26.25 is the force needed to stretch 15 inches which is m.
To approach this problem, we can use the concept of proportionality.
If the length a spring stretches is directly proportional to the force applied, we can write the proportional equation as:
force / length = constant
Let's denote this constant as k.
Now, we have the following information:
Force (x) = 7 pounds
Length (h) = 4 inches
Using this information, we can calculate the value of the constant k:
7 / 4 = k
k = 1.75
To find the force necessary to stretch the same spring m inches, let's denote it as F_m:
F_m / m = k
Substituting the given values:
F_m / 15 = 1.75
To solve for F_m, we can multiply both sides of the equation by 15:
F_m = 1.75 * 15
F_m = 26.25
Therefore, the force necessary to stretch the same spring 15 inches is approximately 26.25 pounds.
To find the force necessary to stretch the spring m inches, we can use the concept of a proportion. Since we are told that the length a spring stretches is directly proportional to the force applied, we can set up the following proportion:
Force / Length = Force / Length
Let's substitute the given values into the proportion:
x / h = Force / m
We are given that x = 7 and h = 4, so let's insert those values:
7 / 4 = Force / 15
Now, we can cross-multiply to solve for the Force:
7 * 15 = 4 * Force
105 = 4 * Force
To find the Force, divide both sides of the equation by 4:
Force = 105 / 4
Now, we can calculate the value of Force:
Force = 26.25
Therefore, the force necessary to stretch the same spring 15 inches is 26.25 pounds.