Please help with this long response ap question

Question

Block 1 is resting on the floor with block 2 at rest on top of it. Block 3, at rest on a smooth table with negligible friction, is attached to block 2 by a string that passes over a pulley, as shown above. The string and pulley have negligible mass.

Block 1 is removed without disturbing block 2.

i. Consider the scenario where the mass  m3 of block 3 is greater than the mass  m2 of block 2. Without using equations, make a claim about the motion of block 3 in terms of balanced or unbalanced forces.

ii. Derive an equation for the acceleration of block 3 for any arbitrary values of  m3 and  m2. Express your answer in terms of  m3,  m2, and physical constants as appropriate.

(c) Describe in what way your answer to part (b)(ii) is or is not consistent with your claim in part (b)(i).

Answer 1

i ) Block 3 will be accelerated to the side by the string as block 2 starts to fall towards the floor. Since the string cannot stretch , the magnitude of the acceleration of block 2 and block 3 will be the same.

ii) The free body diagram for block 3 leads to the Newton's equation T = m₃ a (where T is the tension in he string)

The free body for block 2 leads to the Newton's equation m₂ g - T = m₂ a

Solving this set of two equations with the two unknowns a and T gives

a = [ m₂ /(m₂ + m₃) ] g and T = m₃ m₂ g /(m₂ + m₃)

iii) The value of the acceleration a is reasonable. It is very low if m₂ is small relative to m₃

and equal to g if m₃ is small. In this latter case, the m₃ just follows m₂