Two identical objects A and B of mass M move on a one-dimensional, horizontal ai

Question

Two identical objects A and B of mass M move on a one-dimensional, horizontal air track. Object B initially moves to the right with speed v0. Object A initially moves to the right with speed 3 v0, so that it collides with object B. Friction is negligible. Express your answers to the following in termsof M and v0.

When the experiment is performed, the student is surprised to observe that the objects separate after the collision and that object B subsequently moves to the right with a speed 2.5 v0.
Q -- Determine the kinetic energy dissipated in the actual experiment.

Explanation / Answer

Here ,

for two idential objects,

let the final speed of object A is vA

initial speeds ,

uA = 3 v0

uB = v0

final speed of B

vB = 2.5 v0

Using conservation of momentum

M *(vA + vB) = M *(uA + uB)

2.5 v0 + vA = 3 * v0 + v0

vA = 1.5 v0

kinetic energy dissipated = initial kinetic energy - final kinetic eneryg

kinetic energy dissipated = 0.5 * M * (v0^2 + (3 v0^2)) - 0.5 * M * ((2.5 v0)^2 + (1.5 v0)^2)

kinetic energy dissipated = M * v0^2 * 0.5 *(10 - 2.5^2 - 1.5^2)

kinetic energy dissipated = 0.75 * M*v0^2

the kinetic energy dissipated in the actual experiment is 0.75 * M*v0^2

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