Question

A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 31.0 ∘ above the horizontal. The glider has mass 7.00×10−2 kg . The spring has 590 N/m and negligible mass. When the spring is released, the glider travels a maximum distance of 1.80 m 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? b) When the glider has traveled along the air track 0.800 m 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?

Answer 1

M = 7.00 * 10^-2 kg
k = 590 N/m
Vertical height travelled h = 1.80 m * sin(theta) = 1.80 m * sin(31) = 0.927 m
By conservation of energy,
1/2 * k * x^2 = Mgh
1/2 * 590 * x^2 = 7.00 * 10^-2 * 9.8 * 0.927
295*x^2 = 0.6359
x^2 = 2.155*10^-3
x = sqrt(2.155*10^-3) = 0.046 m

so spring was originally compressed 0.046 m

and kinetic energy at this point is zero.