Question

Two blocks with different masses are attached to either end of a light rope that passes over a light, frictionless pulley suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended 1.20 𝑚, its speed is 3.00 𝑚/𝑠. If the total mass of the two blocks is 22.0 𝑘𝑔, what is the mass of each block? 

Answer 1

1) Determine the acceleration of the two blocks:

$$a=\frac{v^2}{2h}.$$

2) Apply Newton's second law for both blocks (assuming positive direction is upward):

$$m:ma=T-mg,\\ M:-Ma=T-Mg,$$

subtract the lower equation from the upper:

$$ma-(-Ma)=T-mg-T+Mg,\\ m(a+g)=M(g-a),\\\space\\ m=M\frac{g-a}{g+a}=M\frac{g-[v^2/(2g)]}{g+[v^2/(2g)]}=9.82\text{ kg}.$$