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On a frictionless horizontal air table, puck A (with mass 0.251 kg ) is moving toward puck B (with mass 0.371 kg ), which is initially at rest. After the collision, puck A has velocity 0.120 m/s to the left, and puck B has velocity 0.654 m/s to the right.

What was the speed vAi of puck A before the collision?

Calculate ΔK , the change in the total kinetic energy of the system that occurs during the collision.

Respuesta :

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(a) The speed  of puck A before the collision is determined as 0.847 m/s.

(b) The change in the total kinetic energy of the system that occurs during the collision is 0.009 J.

Speed of puck A before the collision

The speed of puck A before the collision is calculated from the principle of conservation of linear momentum as follows;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

0.251u₁ + 0.371(0) = 0.251( -0.12) + 0.371(0.654)

0.251u₁ = 0.2125

u₁ = 0.2125/0.251

u₁ = 0.847 m/s to the right

Change in the total kinetic energy of the system

Initial kinetic energy = ¹/₂ x 0.251 x (0.847)² + ¹/₂ x 0.371 x (0) = 0.09 J

Final kinetic energy = ¹/₂ x 0.251 x (-0.12)² + ¹/₂ x 0.371 x (0.654)² = 0.081 J

ΔK.E = 0.081 - 0.09 = 0.009 J ≈ 0 J

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