An ideal massless spring S can be compressed $$1$$ m by a force of $$100N$$ in equilibrium .The same spring is placed at the bottom of a frictionless inclined plane at $$30o$$ to the horizontal. A $$10kg$$ block M is releases from rest at the top of the incline and is brought to rest momentarily after compressing the spring by $$2m$$. If g $$=$$ $$10$$ $$ms-2$$, what is the speed of mass just before it touches the spring?

Question

An ideal massless spring S can be compressed $$1$$  m by a force of $$100N$$ in equilibrium .The same spring is placed at the bottom of a frictionless inclined plane at $$30o$$ to the horizontal. A $$10kg$$ block M is releases from rest at the top of the incline and is brought to rest momentarily after compressing the spring by $$2m$$. If g $$=$$ $$10$$ $$ms-2$$, what is the speed of mass just before it touches the spring?

Infinity Learn · Accepted Answer

restoring force of a spring is $$F=-$$$$kx$$∴spring constant is $$k=Fx=1001=100N/maccording$$ to principle of conservation of energy, when $$mass=10kg$$ slide down $$inclineEinitial=EfinalKEMass+PEMass=energy$$ stored in a spring∴$$12$$×$$10$$×$$v2+10102sin300=12$$×$$100$$×$$22solving$$ we get velocity of mass is V $$=$$ $$20m/s$$

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