A force of 10N stretches an elastic spring to a total length of 20cm. If an additional force of 8N stretches the spring 4cm further, calculate the natural length of the spring.
Let X be the natural length of the spring.
According to Hooke's Law, the force applied to stretch a spring is directly proportional to the extension produced.
So, the force required to stretch the spring from its natural length X to 20cm is 10N.
Therefore, we can write:
10N = k(20cm - X)
Solving for k:
k = 10N / (20cm - X)
Now, the force required to stretch the spring an additional 4cm from 20cm to 24cm is 8N.
Therefore, we can write:
8N = k(24cm - X)
Substitute the value of k into the equation:
8N = (10N / (20cm - X))(24cm - X)
Simplify:
8N = (240cm - 10X) / (20cm - X)
8N(20cm - X) = 240cm - 10X
160cm - 8X = 240cm - 10X
2X = 80cm
X = 40cm
Therefore, the natural length of the spring is 40cm.