Choice of motor or actuator depends on the construction details (pulley and rope friction, etc.) so build the setup, and measure the force required to perform the action at the required speed.
Buy an actuator and controller that can comfortably provide at least twice that measured force.
You plan to lift a weight, but then what? Hold it? Let it return to it's original location? How will you know when it has been lifted? How will you know if the rope slips on the drive pulley? Will you need to repeat the lifting?
How heavy is the counterweight?
Consider that the motor has to hold the weight of the counterweight if you disconnect the load (the weight you are lifting). Counterweight would commonly be 1/2 the maximum load, so that the force needed to lift the counterweight with no load is roughly equal to the force needed to lift the load at maximum load.
So my plan is this: The motor lifts the weight to a precise point between 0 an 4m. He holds it there for like a minute, and than he moves it to another point inbetween 0 and 4m.
Ok, I already tried to calculate this by myself, but I guess I’m to dumb for it. And aren’t there any possibilities to control the motor with an Arduino?
If ignoring friction and rope (or cable) bending losses the the question is how fast do you need to accelerate? Or in what distance will the load have to travel before reaching the speed goal.
Question for you..... knowing
F = ma what m (mass) would you think goes into this equation? 50 kg or 100 kg?
Also you need to be more specific on what you expect to happen (in text form).
For instance:
A button it pushed
the motor accelerates the load to 1m/s then does it keep accelerating? If so for how long?
What function is the Arduino bring to the actions?
In your original post you state (ask)
Can I control it using Arduino?
You need to sit back and think about what "control" you are thinking of. For whatever reason you are doing this, it will end up being a learning experience. So imagine someone offered you a brand new latest version X-Box, but you have to fully describe what will happen. So sit back and think this through with the mindset that the only things that will happen are what you describe.
Thank you for your help, I will try to explain you my plan as good as possible:
The construction should be capable to move the weight to a specific hight between 0 and 4 meters. For example, I want to type „243“ into my PC, which then sends the data to an Arduino, which controls the motor. The motor should be capable to move the weight in less than a second to the given height (2m 43cm), and stay there until I give the computer a new height.
You can imagine it a bit like an elevator. I hope that now you understand better what I mean…
(Sorry for bad english)