Answer:
Explanation:
To calculate the work done in compressing the spring from its natural length to a length of 9 inches, you can use Hooke's Law, which states that the force required to compress or extend a spring is directly proportional to the displacement from its natural length.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force (in pounds)
k is the spring constant (a measure of stiffness)
x is the displacement from the natural length (in inches)
First, let's find the spring constant (k) using the information provided:
When the spring is compressed to 12 inches, a force of 5 pounds is required.
F = 5 pounds
x = 12 inches
Now, solve for k:
5 = k * 12
k = 5 / 12
Now that you have the spring constant (k), you can calculate the work done to compress the spring to 9 inches from its natural length (15 inches). The displacement (x) is 15 - 9 = 6 inches.
W = (1/2) * k * x^2
W = (1/2) * (5/12) * (6^2)
W = (1/2) * (5/12) * 36
W = (5/24) * 36
W = (5/24) * 36
W = 5 * 3
W = 15 foot-pounds
So, the work done in compressing the spring from its natural length to a length of 9 inches is 15 foot-pounds.