Question

Two boxes are connected by a light string that passes over a light, frictionless pulley. One that rises at 30.0 degrees above the horizontal, and the system isreleased from rest. Find the acceleration of each box? 50.kg box and 30.0kg box

Answer 1

Given that the masses are M₁ = 50.0 Kg and M₂ = 30.0 KgThe angle of inclination is θ = 30.0⁰------------------------------------------------------------------------------------Let the mass M₁ = 50.0 Kg is moving upwards thenthe situation is as shown in the below figure.since the bodies are moving with the accelaration a then apply Newtons law for eachbody thenFor the mass M₁:T-M₁gsinθ = M₁*a --------------(1)For the mass M₂:M₂g- T = M₂*aT=M₂g -M₂*a--------------(2)From the equations (1) and (2) we getM₂g-M₁*a- M₁gsinθ = M₁*aM₂g-M₁gsinθ = M₁*a+M₂*athen the accelaration a =( M₂g - M₁gsinθ)/(M₁ +M₂)=(30*9.8-50*9.8*sin30)/80=0.6125m/s²Since a is positive, the mass M₁ moving upwards and themassM₂ is moving downwards