Understanding the Concepts
* Spring Force: The force exerted by a spring is directly proportional to its displacement from its equilibrium position. This is described by Hooke's Law: F = -kx, where:
* F is the spring force
* k is the spring constant (force constant)
* x is the displacement from equilibrium
* Work: Work is done when a force causes a displacement. In this case, the work done to stretch the spring is the integral of the force over the distance stretched.
Calculations
1. Convert displacement to meters: 25.2 cm = 0.252 m
2. Calculate the work:
* The work done is the area under the force-displacement curve. Since the force is linear (F = kx), this area is a triangle.
* Area of a triangle = (1/2) * base * height
* In this case, the base is the displacement (0.252 m) and the height is the force at that displacement (F = kx = 12.3 Nm * 0.252 m).
* Work = (1/2) * 0.252 m * (12.3 Nm * 0.252 m)
* Work = 0.389 J (Joules)
Therefore, the work required to stretch the spring 25.2 cm is approximately 0.389 Joules.
