i have a physics question

Question

Two objects are connected by a light string that passes over a pulley. Assuming the pulley and incline are frictionless, find the tension in the string.  m₁ =4 kg , m₂ = 11 kg and θ = 55⁰.

Answer 1

Resolve the forces on the ramp using the weight m₁g and the incline angle. The force parallel to the ramp surface is m₁g sin55. Do a force diagram of both masses. For m₁ the equation is T-m₁gsin55 =m₁a and for m₂ the equation is m₂g-T =m₂a. Now solve for a which can be done by adding the two equations. This gives m₂g- m₁gsin55 = a(m₁ +m₂) =a( 15) and so 15a = 9.8( 11-4sin55). Doing the calculation gives a= 5.04m/s². Using this in the first equation gives T= 4•5.04 + 4•9.8•(.819) = 52.27N.