Question

A 700 g air-track glider attached to a spring with spring constant 12 N/m is sitting...

A 700 g air-track glider attached to a spring with spring constant 12 N/m is sitting at rest on a frictionless air track. A 250 g glider is pushed toward it from the far end of the track at a speed of 170 cm/s . It collides with and sticks to the 700 g glider.

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Answer #1

solution:

m1 = 0.70kg
m2 = 0.250 kg

momentum is conserved
m2*v2 + m1*v1 = (m2 + m1)V here v2=170cm/s =1.7m/s and v1=0 (rest) and V centre of mass velocity
(0.250)(1.7) = (0.95)V

V=0.447 m/s

that is their velocity after the collision
.5Mv² = .5kA² K=12N/m ; M=m1+m2
.5(0.95)(0.447)² = .5(12)A² ; A =amplitude

A=0.125 m ans

time period for spring mass system = 2pi* sqrt(M/k) = 2pi * sqrt(0.95/12) = 1.767s ans

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