Answer :
The work required to stretch the spring is 91.6 Ibs-inch
What is work?
Work is defined as force applied across a distance. Work examples include pushing an object against gravity, driving a car up a hill, and lowering a captive helium balloon. Work is the mechanical expression of energy.
Δx : displacement from equilibrium position
f = k Δ x (force due to spring = -kΔx)
where, k is the spring constant
Given,
f = 20ibs
Δx = 24 -18 Inches = 6 inches
∴ k = 20/6 ibs/inch
Now, PE stored in spring = 1/2 k (Δx)²
Δx : displacement from equilibrium position
Work done = change in PE
= 1/2K (Δx₂)² -1/2k (Δx₁)²
given,
Δx₁ = 21-18 inches = 3 inches
Δx₂ = 26-18 inches = 8 inches
∴work done = 1/2 * 20/6 (8² - 3²)Ibs-inches
=10/6 *5*11
work done = 91.6 ibs-inch
The spring must be stretched with 91.6 Ibs-inch of force.
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