Question

A block of mass m1=3.7kg on a smooth inclined plane of angle 30 is connected by a cord over a small frictionless pulley to a second block of mass m2=2.3kg hanging vertically. Calculate the acceleration of each block

Answer 1

consider the forces on mass m₁ on the incline plane :

parallel to incline , force equation is given as

T - m₁ g Sin30 = m₁ a

T = m₁ g Sin30 + m₁ a                                       eq-1

consider the force on mass m₂ on the incline plane :

m₂ g - T = m₂ a  

T = m₂ g - m₂ a                                                  eq-2

Using eq-1  and eq-2

m₂ g - m₂ a = m₁ g Sin30 + m₁ a

inserting the values

(2.3 x 9.8) - 2.3 a = (3.7 x 9.8) Sin30 + 3.7 a

a = 0.74 m/s²