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 3 0 ∘ to the horizontal. A 10

Question

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 3 0 ∘ 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?

TestHub · Accepted Answer

F = k x ∴ k = x F ​ = 1 100 ​ N / m = 100 N / m Now, from energy conservation, between natural length of spring and its maximum compression state. 2 1 ​ m v 2 + m g h = 2 1 ​ k x m a x 2 ​ ∴ v ​ = m k x m a x 2 ​ ​ − 2 g h ​ = 10 ( 100 ) ( 2 ) 2 ​ − ( 2 ) ( 10 ) ( 2 2 ​ ) ​ = 20 ​ m / s ​

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