A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed $ω$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

Question

Infinity Learn · Accepted Answer

Let say increase in the length of the spring $$=$$ x  ​and L $$=l+x$$ be the total length of the spring during motion. The centripetal force acting on the particle is provided by the spring.​∴mω$$2L$$ $$=$$ $$kx$$⇒mω$$2l+x=$$$$kx$$    ​⇒ $$lx+1=km$$ω$$2$$     ​⇒ $$x=ml$$ω$$2k$$−mω$$2$$

A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed $ω$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

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A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is:

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A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed $ω$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is: