Question

A 500 g air-track glider attached to a spring with spring constant 9.5 N/m is sitting at rest on a frictionless air track. A 230 g glider is pushed toward it from the far end of the track at a speed of 110 cm/s . It collides with and sticks to the 500 g glider.

What is the amplitude of the subsequent oscillations?

What is their period?

Answer 1

here,

mass of glider 1, m1 = 500 g = 0.5 kg

spring constant , K = 9.5 N/m

mass of glider 2 , m2 = 230 g = 0.23 kg

u1 = 110 cm/s = 1.1 m/s

let the speed of combination after the collison be v

using conservation of momentum

m2 * u2 = (m1 + m2 ) * v

0.23 * 1.1 = (0.23 + 0.5) * v

v = 0.35 m/s

let the amplitude of motion be A

using conservation of energy

0.5 * K * A^2 = 0.5 * ( m1 + m2) * v^2

9.5 * A^2 = (0.23 + 0.5) * 0.35^2

solving for A

A = 0.097 m

the amplitude of motion is 9.1 * 10^-2 m

the period of motion , T = 2*pi*sqrt((m1 + m2)/K)

T = 2 *pi * sqrt((0.23 + 0.5) /9.5) s

T = 1.74 s