This is a question I took previously. Some of my colleagues got [MATH]0.3 \ m/s^2[/MATH], but I got [MATH]1.6 \ m/s^2[/MATH]
Here how I did it
let [MATH]g = 10 \ m/s^2[/MATH]
for the big Block, we have
[MATH]2g\sin(37°) - 2g\cos(37°)(0.2) - T = 2a[/MATH]
for the small block, we have
[MATH]T - 1g(0.2) - F = 1a[/MATH]
[MATH]T = a + g(0.2) + F[/MATH]
then
[MATH]2g\sin({37}°) - 2g\cos({37}°)(0.2) - a - g(0.2) - F = 2a[/MATH]
solving for [MATH]a[/MATH]
[MATH]a = \frac{2g\sin({37}°) - 2g\cos({37}°)(0.2) - g(0.2) - F}{1 + 2} = \frac{2(10)\sin({37}°) - 2(10)\cos({37}°)(0.2) - 10(0.2) - 2}{3} = 1.6 \ m/s^2[/MATH]
Did I do anything wrong in my calculations?