The momentum of a moving object:

$\overline{){\mathbf{p}}{\mathbf{=}}{\mathbf{m}}{\mathbf{v}}}$

Conservation of momentum:

$\overline{){{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{v}}}_{\mathbf{0}\mathbf{,}\mathbf{1}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{v}}}_{\mathbf{0}\mathbf{,}\mathbf{2}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{,}\mathbf{1}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{{\mathbf{m}}}_{{\mathbf{2}}}{{\mathbf{v}}}_{\mathbf{f}\mathbf{,}\mathbf{2}}}$

Conservation of kinetic energy:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{(}}{\mathbf{v}}}^{}}$_{0,1}_{0,2}_{f,1}_{f,2}

The objects separate after the collision.

Using conservation of momentum and the variables m_{1} = 2m, m_{2} = m, v_{0,1} = v, v_{0,2} = 0, v_{f,1} = v_{1} and v_{f,2} = v_{2}.

2mv + m(0) = 2mv_{1} + mv_{2}

v_{2} = (2v - 2v_{1}) =

v_{2} = 2(v - v_{1}) --------- Eqn 1

Using conservation of energy:

(1/2)2mv^{2} = (1/2)2mv_{1}^{2} + (1/2)mv_{2}^{2}

v^{2} = v_{1}^{2} + (1/2)v_{2}^{2}

Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary.

Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities v_{1} and v_{2} of objects 1 and 2.

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