(Solved): The Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley ...

The Atwood machine consists of two masses hanging from the ends of a rope that passes over a pulley. Approximate the pulley as a uniform disk with mass $$m_{\mathrm{p}}=6.33\mathrm{kg}$$ and radius $$r_{\mathrm{p}}=0.450\mathrm{m}$$. The hanging masses are $$m_{\mathrm{L}}=21.7\mathrm{kg}$$ and $$m_{\mathrm{R}}=14.5\mathrm{kg}$$. Calculate the magnitude of the masses' acceleration $$a$$ and the tension in the left and right ends of the rope, $$T_{\mathrm{L}}$$ and $$T_{\mathrm{R}}$$, respectively. $$a=\mathrm{m}/{\mathrm{s}}^2$$ $$T_{\mathrm{L}}=$$ $$T_{\mathrm{R}}=$$ $$\mathrm{N}$$