A certain ideal massless spring can be compressed 1.0 m by a force of 100 N. Thi

Question

A certain ideal massless spring can be compressed 1.0 m by a force of 100 N. This spring is placed at the bottom of a frictionless inclined plane, oriented so that it is parallel to the incline. The incline has an angle of theta = 30degree with respect to the horizontal. A 10 kg mass M is released from the top of the incline. The mass slides down the incline, eventually hitting the spring, and is brought to rest momentarily after compressing the spring 2.0 m. Through what distance does the mass slide before coming to rest?

Explanation / Answer

first we need to find k F=kx we know that if F=100 then x=1 m --> k=100 N/m use conservation of energy mgh = kx^2/2 --> h=kx^2/2mg = 100*2^2/2*10*9.8=2.04 m the mas was on height of 2.04 m before stopping the sliding distance is 2.04/tg30=3.53 m

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