Hooke's Law states that the distance a spring will stretch beyond its natural length varies directly with the force applied to the spring. A force of 12 pounds is needed to stretch a certain spring 9 inches beyond its natural length.
Find a formula that models the length a spring will stretch beyond its natural length in inches as a function of the force applied to the string in pounds. (All I could figure out is that the input is the weight and the output is length. I don't know how to find the formula though, please help!!)
k = 12Lbs/9in = 1.33 Lbs/in.
To find the formula that models the length a spring will stretch beyond its natural length, we can use Hooke's Law. Hooke's Law states that the distance a spring will stretch (x) varies directly with the force applied to the spring (F).
Let's denote the length a spring will stretch beyond its natural length as x, and the force applied to the spring as F.
According to Hooke's Law, we know that x varies directly with F. This means we can write the equation as:
x = kF
Where k is the constant of variation.
To find the value of k, we need to use the given information that a force of 12 pounds is needed to stretch the spring 9 inches beyond its natural length.
Substituting the given values into the equation:
9 = k(12)
Now we can solve for k:
k = 9/12 = 3/4
So, the equation to model the length a spring will stretch beyond its natural length is:
x = (3/4)F
To find a formula that models the length a spring will stretch beyond its natural length as a function of the force applied to the string, we can start by looking at the given information and applying Hooke's Law.
Hooke's Law states that the distance a spring will stretch beyond its natural length varies directly with the force applied to the spring. This can be written as:
F = k * x
Where:
- F is the force applied to the spring
- k is the spring constant (a measure of stiffness of the spring)
- x is the distance the spring stretches beyond its natural length
In this case, we are given that a force of 12 pounds is needed to stretch the spring 9 inches beyond its natural length. We can plug these values into Hooke's Law equation to find the value of the spring constant k.
12 = k * 9
To solve for k, divide both sides of the equation by 9:
k = 12/9
Simplifying the right side:
k = 4/3
Now that we have found the value of the spring constant k, we can use it to create a formula that models the length a spring will stretch beyond its natural length as a function of the force applied to the spring.
x = (F * k)
Substituting the value of k we found:
x = (F * 4/3)
So, the formula that models the length a spring will stretch beyond its natural length in inches as a function of the force applied to the spring in pounds is:
x = (4/3) * F