At a munitions factory, chemicals \(M\) and \(P\) have to be added to a vat containing chemical \(\mathrm{C}\). Chemicals \(\mathrm{M}\) and \(\mathrm{P}\) have to be added simultaneously to prevent an accidental detonation. Your task, as the chemical engincer in charge, is to come up with a way of doing this, and you devise the pulley scheme shown in Figure P8.49, where block W is a counterweight whose inertia controls the speed at which the buckets containing chemicals \(M\) and \(\mathrm{P}\) move. The idea is that when a strap holding block \(\mathrm{W}\) at rest is released, the block rises and the buckets containing \(\mathrm{M}\) and \(\mathrm{P}\) descend into the vat. In order to have the two buckets have an identical acceleration of magnitude \(g / 3\), what must be the ratios of the inertias \(m_{\mathrm{W}}, m_{\mathrm{M}}\), and \(m_{\mathrm{p}}\) ? lgnore any friction in the pulleys.

Data from Figure P8.49

Transcribed Image Text:

W M C