Anonymous asked in Science & MathematicsPhysics · 1 month ago

help with physics!?

Consider an elastic, head-on collision between

an object of mass m moving at speed v0 and

an object of mass 3 m, initially at rest. After the collision the mass m moves at a

velocity ~v1 and the mass 3 m at velocity of ~v2,

both along the original line of motion. What are the final velocities ~v1 and ~v2?

The sign on each will determine the direction

of the motion.

Attachment image

1 Answer

  • NCS
    Lv 7
    1 month ago

    For an elastic, head on collision, we know (from conservation of energy) that

    v₀ = v₂ - v₁

    so here v₁ = v₂ - v₀

    Conserve momentum, substituting for v₁:

    m*v₀ = m*(v₂ - v₀) + 3m*v₂ → → mass m cancels

    v₀ = v₂ - v₀ + 3v₂

    2v₀ = 4v₂

    v₂ = v₀ / 2

    You have to choices where this is true, so solve for v₁:

    v₁ = v₀/2 - v₀ = -v₀/2

    making #6 the correct choice.

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