A small glider is placed against a compressed spring at the bottom of an air tra

Question

A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 45.0 degrees above the horizontal. The glider has mass 9.00×10^2 kg . The spring has 610N/m and negligible mass. When the spring is released, the glider travels a maximum distance of 1.50m along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring.

a. What distance was the spring originally compressed?
b. When the glider has traveled along the air track 0.500 from its initial position against the compressed spring, is it still in contact with the spring?
c. What is the kinetic energy of the glider at this point?

Explanation / Answer

a) According to conservation of energy            Ki + Ui = Kf + Uf            m g h sin + 0 = 0.5 k x2 + 0 ==> x = [2 m g h / k ]             = [ 2 x 900 x 9.8 x 1.50 x sin 45 / 610 ]             = 5.538 m b) it looses contact c) According to conservation of energy           m g h' sin + KE = 0.5 k x2           900 x 9.8 x 0.5 x sin45 + KE = 0.5 x 610 x 5.538 x 5.538 ==> KE = 6235.84 J

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