Let's say we ignore the friction for simplicity now, and assume mass of counter weight 600kg, this should be the weight of elevator plus cable and depending on the traffic pattern some extra weight.
More important than the speed is what acceleration you need. Say we choose 4m/s otherwise at constant speed of 10m/s we just need much smaller tension of holding the difference weight of 2000- 600=1400kg. So the tension would be only 13729N and torque would be 6860N.m, but we will see the torque needed to accelerate the elevator is much larger.
The tension force in the cable to accelerate the elevator and its counter weight is
$$ F_{net} = T_{cable} - mg = m\alpha $$ $$ and \ F_{net}= \ m\alpha = 2600* \alpha = 2600*4 = 10400N $$
So:
$$ T_{cable}= 10400 + mg =10400 + 1400 *9.8 = 24120N $$
now we can calculate the torque
$$ \tau = f*r = 24120 * 0.5 = 12060 N.m $$
So we see the torque needed to accelerate the elevator is nearly two times that which is needed to move it at 10m/s. The real scenario is each manufacturer uses their own proprietary pattern of relays and controls that adjust the acceleration in a curve , ramping up, for comfort and minimizing wear and tear.