Two disks collide on a frictionless tabletop

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Linear Momentum · Linear Momentum

Problem

Two disks collide on a frictionless tabletop. Disk 1 (mass 0.25 kg0.25\,\text{kg}) initially moves with velocity components (1.8 m ⁣⋅ ⁣s−1 east, 0.0 m ⁣⋅ ⁣s−1 north)(1.8\,\text{m}\!\cdot\!\text{s}^{-1}\text{ east},\,0.0\,\text{m}\!\cdot\!\text{s}^{-1}\text{ north}). Disk 2 (mass 0.35 kg0.35\,\text{kg}) initially moves with velocity components (0.0 m ⁣⋅ ⁣s−1 east, 2.0 m ⁣⋅ ⁣s−1 north)(0.0\,\text{m}\!\cdot\!\text{s}^{-1}\text{ east},\,2.0\,\text{m}\!\cdot\!\text{s}^{-1}\text{ north}). After the collision, disk 1 moves with components (1.2 m ⁣⋅ ⁣s−1 east, 1.0 m ⁣⋅ ⁣s−1 north)(1.2\,\text{m}\!\cdot\!\text{s}^{-1}\text{ east},\,1.0\,\text{m}\!\cdot\!\text{s}^{-1}\text{ north}), and disk 2 with components (0.6 m ⁣⋅ ⁣s−1 east, 1.0 m ⁣⋅ ⁣s−1 north)(0.6\,\text{m}\!\cdot\!\text{s}^{-1}\text{ east},\,1.0\,\text{m}\!\cdot\!\text{s}^{-1}\text{ north}). Determine whether the collision was elastic by calculating the change in total kinetic energy of the two-disk system (state the numerical value and its sign).

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