Question

The diagram below shows an Atwood's Machine: Mass A (5 kg) and Mass B (1.5 kg) are attached to a frictionless, massless pulley.
Hint: These situations can be tricky or easy depending on how you view the problem. For practice with algebra, think of each mass as separate but having a common acceleration. For ease of computation, think of the whole mass-cord-mass thingy as a single object.

(a) What is the acceleration of Block A when the blocks are released?
(b) How long will it take for block A to fall 3 m?

Answer 1

\[\large \sum F_{yb} = T - m_b g = m_b a\]
\[\large \sum F_{ya} = T - m_a g = m_a a\]

So we get.
\[T = m_ba - m_bg\]
\[m_b a-m_b g - m_a g = m_a a \rightarrow \large a = \frac{-m_b g - m_a g}{m_a - m_b}\]

We got the acceleration, now you do the b.