a certain coiled spring with an unstretched length of 20cm require a force of 2N to stretch it by 0.2cm. What is the work done in stretching it by 2cm. If the elastic limit is nt execeed.
F = 2N/0.2cm * 2cm = 20 H.
Work = F*d.
To find the work done in stretching the spring by 2cm, we need to understand the concept of work done and use Hooke's Law. Let's break down the steps to solve this problem:
Step 1: Understand Hooke's Law
Hooke's Law states that the force required to stretch or compress a spring is directly proportional to the displacement from its original position. Mathematically, it can be expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.
Step 2: Find the spring constant
Given that the force required to stretch the spring by 0.2cm (or 0.002m) is 2N, we can use Hooke's Law to find the spring constant.
2N = k * 0.002m
k = 2N / 0.002m
k = 1000 N/m
Step 3: Calculate the work done
Now that we have the spring constant, we can calculate the work done in stretching the spring by 2cm (or 0.02m). The work done is defined as the product of force and displacement and can be calculated using the equation W = F * x.
Since the force and displacement are not constant throughout the stretch, we need to use calculus to find the total work done. We can divide the stretch into small increments and calculate the work done for each increment. Then, we can sum up all these small increments to find the total work done.
W_total = ∫(F dx)
where,
W_total is the total work done,
F is the force at each increment, and
dx is the small change in displacement.
For each small increment, the force can be calculated using Hooke's Law:
F = k * x
Integrating the equation, we get:
W_total = ∫(kx dx)
W_total = k/2 * x^2
Therefore, the work done in stretching the spring by 2cm is:
W_total = (1000 N/m) / 2 * (0.02m)^2
W_total = 100 J (Joules)
So, the work done in stretching the spring by 2cm is 100 Joules, given that the elastic limit is not exceeded.