A spring has an unstretched length of 4.50 cm. The spring is fixed at one end and a force of35.0 N is applied to the other end so that the spring extends.The spring obeys Hooke’s law and has a spring constant of 420 N m–1 .What is the strain of the extended spring?A 0.019 B 0.083 C 1.85 D 2.67
Question
A spring has an unstretched length of 4.50 cm. The spring is fixed at one end and a force of35.0 N is applied to the other end so that the spring extends.The spring obeys Hooke’s law and has a spring constant of 420 N m–1 .What is the strain of the extended spring?A 0.019 B 0.083 C 1.85 D 2.67
Solution
To calculate the strain of the extended spring, we first need to find the extension of the spring.
Hooke's law states that the force (F) applied to a spring is directly proportional to the extension (x) of the spring. This can be written as F = kx, where k is the spring constant.
We can rearrange this equation to find the extension: x = F/k.
Substituting the given values, we get x = 35.0 N / 420 N/m = 0.083 m or 8.3 cm.
Strain is defined as the change in length (extension) divided by the original length. So, strain = x / original length.
Substituting the values, we get strain = 8.3 cm / 4.5 cm = 1.85.
So, the strain of the extended spring is 1.85 (Option C).
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