An ideal massless spring S can be compressed 1 m by a force of 100 N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at 30^ to the horizontal. A 10 kg block M is released from rest at the top of the incline and is brought to rest momentarily after co

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

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Correct answer: A. 20 ~m / s

F=k x k= F x = 100 1 ~N / m =100 ~N / m Now, from energy conservation, between natural length of spring and its maximum compression state. 1 2 m v^2+m g h= 1 2 k x_ ^2 aligned v & = k x_ ^2 m -2 g h \ & = (100)(2)^2 10 -(2)(10) ( 2 2 ) = 20 ~m / s aligned

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