Answer to Question #240093 in Physics for sunwoo

Question

A 20 kg block (m1) and a bucket with mass m2 are connected by a light string that passes over a frictionless pulley as shown in Figure 2. The block lies on an incline plane of angle, α = 53.1° and the coefficient of kinetic friction between the block and the plane is 0.40. Calculate the mass of the hanging bucket, m2 if it is moving downward with the acceleration of 2.67 m/s2 

Answer 1

$N-mg\cdot\cos53.1°=0$

$T-mg\cdot\sin53.1°-\mu N=ma$

$T-Mg=-Ma$

From these equations $M=\frac{m(a+g\cdot\sin53.1°+\mu mg \cdot \cos53.1°)}{g-a}=$

$=\frac{20\cdot(2.67+9.8\cdot\cdot\sin53.1°+0.4\cdot 20\cdot9.8 \cdot \cos53.1°)}{9.8-2.67}=36\ (kg)$