I'm struggling with the above question.
As it is a smooth table, there should be no friction, so I came up with the two equations (using $F=ma$):
$T=5a$ and $T=(2*9.8)+2a$.
This solved out to give me the answer of $a = 6.5333333$; however, the back of the book states the answer is 2.8.
What have I done wrong?
First you should treat the T as unknown and for g is the gravitational acceleration 2g-T=2*a then T=2g-2a using the last equation insert in the equation for the force on the mass on the table which is 5*a=T. Why you are treating the T as unknown initially is because you know the gravitational force on the hanged mass and you don't know the acceleration because you don't know the total force on the hanged mass because total force effecting on hanged mass is 2*g-T=Ftotal. Rest is just calculation.