One end of an ideal spring is fixed at point O and other end is attached to a small disc of mass m which is given an initial velocity $$v0$$ perpendicular to its length on a smooth horizontal surface. If the maximum elongation of the spring is $$l04$$ then $$($$ $$l0$$ $$=$$ natural length, k $$=$$ stiffness of the $$spring)$$ (initially$$ the spring is in it’s natural $$length)

Question

One end of an ideal spring is fixed at point O and other end is attached to a small disc of mass m which is given an initial velocity $$v0$$  perpendicular to its length on a smooth horizontal surface. If the maximum elongation of the spring is  $$l04$$  then $$($$ $$l0$$ $$=$$ natural length, k $$=$$ stiffness of the $$spring)$$ (initially$$ the spring is in it’s natural $$length)

Infinity Learn · Accepted Answer

According to Conservation of Angular Momentum  m×$$v0$$×$$l0=m$$×v×$$l0+l04$$⇒$$v=4v05According$$ to conservation energy $$12mv02=12mv2+12kx2$$⇒$$mv02=m4v052+kl042$$⇒$$v0=5l012km$$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material