hi all this is an term project i stuced on , i know how to calculate the stresses and all things about the gears (spur)\ but i dont know how to begin with that pls , can you give me hints on how to begin ? what is the relation between power input & speed and the geometry of the input gear

The answer for your Q "what is the relation between power input & speed and the geometry of the input gear" Use Torque = Force * diameter. . . relation to find the force on input shaft. You can use the standard "power-torque-speed" relation if you dont know the torque.

As the original poster asked this back in November and hasn't been seen here since, I suspect that he either figured it out or flunked the term project. The question was so vague, though, that (unless he wasn't a native English speaker and couldn't communicate well) I doubt he understood the problem.

I do not think the question was vague. It is a classic example of a complete gearbox design problem, where the input power, the driven load at the output, the number of stages and the overall envelope of the gearbox is given. The design has to evolve through a number of iterations before it satisfies the given constraints. But isn't the lifting speed of load at 6 ft/s too high? could it be 6 ft/Min?