An ideal massless spring can be compressed by 1 m by a force of 100 N. The same spring is placed at the bottom of a frictionless inclined plane which makes an angle θ = 3 0 ∘ with the horizontal. A 10

Question

An ideal massless spring can be compressed by 1 m by a force of 100 N. The same spring is placed at the bottom of a frictionless inclined plane which makes an angle θ = 3 0 ∘ with the horizontal. A 10kg mass is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring 2 meters. Through what distance (in m ) does the mass slide before coming to rest ?

TestHub · Accepted Answer

k = 100 N/m (1 m compression by 100 N) Energy conservation from release to maximum compression: m g sin θ ⋅ d = 2 1 ​ k x 2 10 × 10 × sin 30° × d = 2 1 ​ × 100 × 2 2 50 d = 200 , so d = 4 m

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