Two blocks are initially in contact sliding down an inclined surface of inclination 30^ , where the 4.0 kg block is lower on the incline than the 2.0 kg block. The friction coefficient between the block of mass 2.0 kg and the incline is ₁ = 0.30 , and that between the block of mass 4.0 kg and the incline is ₂ = 0.20 . Determine the acceleration of the 2.0 kg block. Take g = 10 m/s ^2 .

Step-by-step solution

Let the independent accelerations of the 2.0 kg and 4.0 kg blocks be a₁ and a₂ respectively. For the 2.0 kg block (which is higher on the incline): a₁ = g 30^ - ₁ g 30^ a₁ = 10 1 2 - 0.30 10 3 2 a₁ = 5 - 1.5 1.732 = 5 - 2.598 = 2.402 m/s ^2 For the 4.0 kg block (which is lower on the incline): a₂ = g 30^ - ₂ g 30^ a₂ = 10 1 2 - 0.20 10 3 2 a₂ = 5 - 1.732 = 3.268 m/s ^2 Since a₂ > a₁ and the 4.0 kg block is lower on the incline, the two blocks will separate and move independently. Therefore, the acceleration of the