Question

Find an expression for the acceleration of m1. The pulleys and masses are frictionless. Hint: Think carefully about the relation between the acceleration of the two masses.

Answer 1

It's question #4 on the attached file.

Answer 2

By Newton's second law,
For m1,
\[T={m_1{}a_1}\]
Where T is the tension in the string.
For m2,
\[m_2 g -2T = m_2 a_2\]
from the first equation, we substitute for T and solve for a1
\[a_1 = \frac{ m_2 (g-a_2) }{ 2m_1 }\]
This is what we get.