Eight and one-half foot-pounds of work is required to compress a spring 3 inches from its natural length. Find the work required to compress the spring an additional one-half inch. (Round your answer to two decimal places.)
3.07
To find the work required to compress the spring an additional one-half inch, we can use Hooke's Law, which states that the work required to compress or extend a spring is directly proportional to the displacement from its natural length.
Given that 8 and one-half foot-pounds of work is required to compress the spring 3 inches from its natural length, we can set up a proportion to find the constant of proportionality:
(original displacement) : (original work) = (additional displacement) : (additional work)
Substituting the given values:
3 inches : 8.5 foot-pounds = 0.5 inches : x (foot-pounds)
Next, we can cross-multiply and solve for x:
3 * x = 8.5 * 0.5
x = (8.5 * 0.5) / 3
x ≈ 1.42 foot-pounds
Therefore, the work required to compress the spring an additional one-half inch is approximately 1.42 foot-pounds.