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Problem: 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 v1 and v2 of objects 1 and 2.

FREE Expert Solution

The momentum of a moving object:

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

Conservation of momentum:

Conservation of kinetic energy:

$\overline{)\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{m}}}_{{\mathbf{1}}}{{\mathbf{\left(}}{\mathbf{v}}}^{}}$0,1)2 + 12m2(v0,2)2 = 12m1(vf,1)2 + 12m2(vf,2)2

The objects separate after the collision.

Using conservation of momentum and the variables m1 = 2m, m2 = m, v0,1 = v, v0,2 = 0, vf,1 = v1 and vf,2 = v2.

2mv + m(0) = 2mv1 + mv2

v2 = (2v - 2v1) =

v2 = 2(v - v1) --------- Eqn 1

Using conservation of energy:

(1/2)2mv2 = (1/2)2mv12 + (1/2)mv22

v2 = v12 + (1/2)v22

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Problem Details

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 v1 and v2 of objects 1 and 2.

What scientific concept do you need to know in order to solve this problem?

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