Anyone has any idea how to solve this task ?
I will try to solve it in paper, but I am a little busy until next week or the following. Try calculating the angular speed needed to lift the Weight at 0,08 m/s. With that angular speed and the Motor´s one, you obtain the ratio of the gearbox.
After that, calculate the torque needed for the lead screw, and multiply/divide by the gearbox factor to obtain the Motor torque. That Motor torque and the motor angular speed would give you the Power required for the Motor.
Look for different mechanical eng. books such as the Shingley´s where you can find all the formulas to caclualte torques, lead screws and transmissions.
Let me know if you still needing more help,