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 41.0 above the horizontal. The glider has mass 9.00×102 kg . The spring has 680 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.

Part A

What distance was the spring originally compressed?

Part B

When the glider has traveled along the air track 0.300 m from its initial position against the compressed spring, is it still in contact with the spring?

Part C

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

Explanation / Answer

here,

mass of glider, m = 0.09 kg
inclined angle, A = 41 degrees
spring constant, k = 680 N/m

maximum travelled by glider, d = 1.30 m

Part A:
From Conservation of Energy,
potential Energy in spring = PE gained by glider
mg*D*Sin41 = 0.5 * k * x^2

solving for compressed distance, x

x = sqrt(mg*D*Sin41/k)
x = sqrt(0.09*9.81*1.30*Sin41/680)
x = 0.033 m

Part B:
no, as 0.30 m > 0.033

Part C:
height gained, at this point h = 0.3 *Sin41 = 0.197 m

From Conservation of Energy,
KE = PE of Spring - potential Energy gained by glider
KE = 0.5*k*x^2 - mg*h
KE = 0.5 * 680*0.033^2 - 0.09*9.81*0.197
KE = 0.196 J

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