idea about the single object suspended by a cable

Of course! you know very well about this topic, but i would like some idea particularly about this topic. Please, observe below figure carefully, then we find out that in normal
manner, the tension T in cable is always balanced by the weight of the object so that T-mg=0

T=mg
But when the cable is pulled upwards with some external force 'F' then the new tension T' arises
i.e., T'-mg=ma or T'=m(g+a)
When the cable is lowered down with the same external force 'F' then the new tension T'' arises
i.e., mg-T''=ma or T''=m(g-a)