The net force on the larger mass in the horizontal direction (where we take the direction of F to be positive) is
F - T = 2Ma
where T is the magnitude of tension and a is the mass's acceleration.
The net force on the smaller mass in the vertical direction (upward is positive) is
T - Mg = Ma
If M = 1.0 kg and F = 60 N, then we end up with two equations with two unknowns,
60 N - T = (2.0 kg) a
T - (1.0 kg) (9.8 m/s²) = (1.0 kg) a
Eliminate a and solve for T :
(60 N - T) - 2 (T - (1.0 kg) (9.8 m/s²)) = (2.0 kg) a - 2 (1.0 kg) a
60 N - T - 2T + 19.6 N = (2.0 kg) a - (2.0 kg) a
40.4 N - 3T = 0
3T = 40.4 N
T = (40.4 N) / 3
T ≈ 13 N
