A glider of mass 0.250 kg moves on a horizontal frictionless air track. It is pe

Question

A glider of mass 0.250 kg moves on a horizontal frictionless air track. It is permanently attached to one end of a massless horizontal spring, which has a force constant of 11.0 N/m both for extension and for compression. The other end of the spring is fixed. The glider is moved to compress the spring by 0.180 m and then released from rest.

(a) Calculate the speed of the glider at the point where it has moved 0.180 m from its starting point, so that the spring is momentarily exerting no force.
??? m/s
(b) Calculate the speed of the glider at the point where it has moved 0.250 m from its starting point.
??? m/s

Explanation / Answer

(a) COservation of energy

0.5 k x^2 = 0.5 m v^2

v = x sqrt(k/m)

v = 0.18 * sqrt(11/0.25) = 1.194 m/s

(b) At 0.25 m

0.5 m v^2 = 0.5 m v1^2 - 0.5 k (0.25-0.13)^2

v = sqrt( v1^2 - (k/m)*(0.25-0.13)^2)

v = sqrt(1.194^2 - (11/0.25)*(0.25-0.13)^2) = 0.89 m/s

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