Find acceleration

Question

Block m₁ = 6 kg and lies on an incline plane with a coefficient of kinetic friction of 0.15. m₁ is connected to mass m₂ by a massless rope passing over a pulley.  As m₂moves down, determine the acceleration of m₁ up the incline, given θ = 29⁰ and m₁= m₂.

Answer 1

m₂g - T = m₂a

T - m₁gsinθ - µm₁gcosθ = m₁a

T is tension in rope, g = 9.8m/s^2 accelaration of gravty,

µ - coefficient of kinetic friction,

If we add these equations we get: g(m₂ - m₁sinθ - μm₁cosθ) = (m₁+m₂)a

from here accelaration a = g(m₂ - m₁sinθ - μm₁cosθ)/(m₁+m₂)

a = 9.8m/s^2(6kg - 6kgsin29^°- 0.15•6kgcos29^°)/(6kg + 6kg) ≅ 1.88m/s^2

Answer 2

general answer for this kind of problem:

https://www.wyzant.com/resources/answers/718129/what-is-the-acceleration-of-boxes-as-they-move-down-the-incline