Question

A 800 g air-track glider attached to a spring with spring constant 14.0 N/m is sitting at rest on a frictionless air track. A 400 g glider is pushed toward it from the far end of the track at a speed of 124 cm/s . It collides with and sticks to the 800 g glider.

Part A

What is the amplitude of the subsequent oscillations?

Part B

What is their period?

Answer 1

Spring constant = k = 14 N/m

Mass of the air track glider pushed toward the spring = m₁ = 400 g = 0.4 kg

Mass of the air track glider attached to the spring = m₂ = 800 g = 0.8 kg

Speed of the air track glider before the collision = V₁ = 124 cm/s = 1.24 m/s

Speed of both the air track gliders after the collision = V₂

By conservation of linear momentum,

m₁V₁ = (m₁ + m₂)V₂

(0.4)(1.24) = (0.4 + 0.8)V₂

V₂ = 0.413 m/s

Amplitude of the resulting motion = A

The kinetic energy of the gliders is converted into potential energy of the spring at maximum displacement.

kA²/2 = (m₁ + m₂)V₂²/2

(14)A² = (0.4 + 0.8)(0.413)²

A = 0.121 m

Time period of oscillation = T

T = 1.84 sec

A) Amplitude of resulting oscillation = 0.121 m

B) Time period = 1.84 sec