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 47.0 above the horizontal. The glider has mass 9.00×102 kg . The spring has 610 N/m and negligible mass. When the spring is released, the glider travels a maximum distance of 1.30 m along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring.

What distance was the spring originally compressed?

What is the kinetic energy of the glider at this point?

Please be detailed!

Explanation / Answer

Suppose spring was compressed by distance d initially.

Applying work-energy theorem,

Work done by all forces = change in KE

Work done by gravity + work done by spring = Kf - Ki

(- m * g * L sin47 ) + (k d^2 /2) = 0 - 0

(610) d^2 / 2 = 0.09 x 9.8 x 1.30 x sin47

d = 0.0524 m or 5.24 cm ........Ans

now using theorem until displacement is d alon the track.

(- 0.09 x 9.8 x d x sin47) + (610 x 0.0524^2 /2 ) = K - 0

K = 0.805 J

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