I need an electric motor....?

How fast does the gate need to be lifted, and how many feet?

Motor HP will then be... (3000lb * (lift in ft) / sec) * (1HP/ 550ft-lb/sec)

Say the gate lift is 10 ft and you want to raise it in 20 sec:

.... (3000lb * 10 ft / 20 sec) * (1HP/ 550ft-lb/sec) = 2.73 HP or 2025kW.

That's a large motor. May I suggest you use a counterweight?

EDIT: From your numbers I get 0.227HP, just a wee bit less than 1/4 HP. A 4x4 off-roader's winch could do this easily and it can take that much static loading, plus it's reversible. Bonus... it can have battery backup.

On the other hand I don't think a fractional-HP gearmotor by itself will do that for you because you expect to put a 3000lb static load on the shaft.

Amother thought... how about a hydraulic system? I'm inclined to think this would be safer than a pulley+cable.

First determine the power to lift the gate...

One HP is 550lb one ft in one second, so 0.0416ft x 1s x 3000/550 = 0.22HP or 167W. With that sort of gearing you will have maybe 50% loss, more like 70% with a worm drive, so allow for the nearest size bigger than 334W or 0.44 HP. That sounds like at least a 1/2 Hp or 400W motor. Go for a bigger size to allow for less efficient gearbox in cold weather, more losses of a worm drive, motor losses (including voltage drop), and friction in the load. It could be that a 1HP motor is cheaper or has some advantage, if you go the AC path I would recommend that. It is a bit heavy for the 12V battery power, unless you opt for 24V.

This can be AC or DC at the 400W size, though that could be too small. For 12V it would draw about 40A. That sounds like it could be attractive for a solar panel operation. However I would go for a higher rating motor, considering it might be sitting in the sun, and you want continuous operation if someone opens and closes the gate a few times.

Now the torque rating on the gearbox output shaft. The radius is 2 inches (0.166ft) so the torque = 0.166 x 3000 = 500 foot pounds. You might need to consider that for the pulleys belts and coupling too. The radius I took as 2 inches might be different, check that. I agree that a winch mechanism might be more suited. Also that a worm drive is more suited, as it should provide the required braking. What happens if the motor loses power? Maybe that is Ok, but probably not. I wouldn't want a 3000 pound gate comeing down on my car or something. You can get motors with solenoid operated brakes too.

Reversing.

A single phase (with two phases) or three phase motor can be reversed by reversing one phase. There are three phase reversable star delta starters that would do that. For single phase you may have yo make up something with a timer, reversing contactor etc. There are also single phase VFD speed controllers for three phase or single phase motors. Three phase motors are likely to be smaller, could be cheaper, and run on single phase using the VFD. The VFD can control speed, torque, braking, reversing etc. You need limit switches on the gate, maybe dead limits too.

Control? Perhaps a PLC, a microcontroller, relays etc. Depends where your skills lie.

The issues point towards a single phase or three phase solution rather than battery. Look for a winch, or a motor with worm drive and sufficient output torque, maybe a brake. Contact a motor salesman, explain what you want.

Edit:

I agree about the counter weight idea. That changes the torque, but the shafts have to be sized for that weight.

Have fun.

With 3000 # counter weights a 1/4 h.p. gearmotor would easily do. The weights should exactly match the weight of the door unless you want a little more force or speed in one direction. The weight of the gate and counter weights should not be on the output shaft of the gear box. Use a jackshaft with bearings rated for the full 3000# on each end. http://www.grainger.com/ Type in gearmotors in the keyword search box. Also, a 4" pulley rotating at 2.5 RPM's will have a lift speed of 2.6 in/sec. if the 4" pulley is being used as a winch spool, but I don't know what your system looks like.

It is not possible to size a motor for the specified use unless the speed of lifting is given.