Given Information:
Force = f = 1 pound
Stretched length = x = 0.1 ft
Required Information:
Work done = W = ?
Answer:
Work done = 6.05 ft.lb
Step-by-step explanation:
From the Hook's law we know that
f(x) = kx
Where f is the applied force, k is spring constant and x is length of spring being stretched.
k = F/x
k = 1/0.1
k = 10 lb/ft
f(x) = 10x
The work done is given by
W = ∫ f(x) dx
Where f(x) = 10x and limits of integration are (1.1, 0)
W = ∫ 10x dx
W = 10*x²/2
W = 5x²
Evaluating the limits,
W = 5(1.1)² - 5(0)²
W = 6.05 - 0
W = 6.05 ft.lb
Therefore, 6.05 ft.lb work has been done in stretching the spring from its natural length to 1.1 feet beyond it's natural length.