0 \mathrm{m}$, $x_1 = 0 \mathrm{m}$, $x_2 = 8.0 \mathrm{m}$, and $m_2 = 0.10 \mathrm{kg}$. We want to find $m_1$. Plugging in the values, we get:
$2.0 = \frac{m_1(0) + 0.10(8.0)}{m_1 + 0.10}$
Solving for $m_1$, we get:
$m_1 = \boxed{0.15 \mathrm{kg}}$
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