Answer to Question #136691 in Physics for Sasuke

Question

Two blocks of mass m=25 kg and M=20 kg are connected via pulley with a
configuration as shown. Assuming that the surfaces are smooth and the angle θ=
45
. Find the acceleration blocks and tension of the cable.

Answer 1

Apply Newton's second law for M:

$$-Ma=T-Mg.$$

Apply Newton's second law for m:

$$X: ma=T-mg\text{ sin}\theta.$$

The solution will be

$$a=g\frac{M-m\text{ sin}\theta}{m+M}=0.67\text{ m/s}^2,\\\space\\ T=M(g-a)=182.6\text{ N}.$$