Hooke’s law describes an ideal spring. Many real springs are better described by the restoring force , where q is a constant.
Consider a spring with .
It is also .
a. How much work must you do to compress this spring ? Note that, by Newton’s third law, the work you do on the spring is the negative of the work done by the spring.
b. By what percent has the cubic term increased the work over what would be needed to compress an ideal spring? Hint: Let the spring lie along the s-axis with the equilibrium position of the end of the spring at .
Then ∆s = s.
a. The work done by person is
b. The cubical term increases the work by
The work done by force Fs , on the particle if the particle moves in the same direction as that of the force is expressed as follow:
here, is the force and is the small displacement in the direction of the force.
The equation of the spring force is
Suppose the particle move from . Therefore, the work done by the person is negative the work done by spring. Therefore,
Substitute the values and evaluate W.
here, the second part (cubical) gives . Therefore finding the percentage of the second term from the first term
Two identical horizontal springs are attached to opposite sides of a box that sits on a frictionless table. The outer ends of the springs are clamped while the springs are at their equilibrium lengths. Then a force applied to the box, parallel to the springs, compresses one spring by while stretching the other by the same amount. What is the spring constant of the springs?
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