Question

Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In an experiment a rubber band and a spring were placed in a vertical position and a series of having Masses were attached to the free end.

a) Does the rubber band used exhibit Hooke's Law behavior? Why or why not?

b) Does the spring used exhibit Hooke's Law behavior ? Why or why not?

c) Simple Harmonic Motion is oscillatory motion of a system under the influence of a linear restoring force. Would you expect Simple Harmonic Motion for your rubber band system if it is set to oscillate? Would you expect simple harmonic motion for you spring system? Explain.

d) Consider a spin-block that does undergo simple harmonic motion. Where in its motion is the speed of the block the maximum? Where in its motion is the acceleration of the block at maximum? At what point in its motion is the force of the spring the greatest?

e) Why would you expect a non 0 % difference between the k determined from Hooke's law and the k determined from the simple harmonic timing measurements?

f) Write the general formula for the position of the block as a function of time. Write the general formula for the velocity of the block as a function of time. Write the general formula for the acceleration of the block as a function of time. Write the general formula for the force exerted on the block by the spring as a function of time. Write the formula for the Mechanical Energy for the spring block system.

Answer 1

a) rubber band do not exhibit Hooks law. For Hooks law for small changes stress/strain must be const. In case of rubber band it can stretch several time to its original length and returns to original length when the external force is removed, it elastic but the const. of proportionality is not there. hence it does not follow Hooks law

b) In the case of spring F = -k x , where k is the spring const. In this case the proportionality is maintained and hence the spring exhibits Hooks law.

c) As explained above in the case of spring, the displacement is proportional to the external force or the acceleration a x - the displacement and hence the motions is simple Harmonic. In case of rubber band the elongation is not proportional to the external force, when the external force is removed the rubber band does not retrace the path of stretching. The motion is not simple harmonic.