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Your question doesn't make sense as it is written, but if the real question is what size generator do you need to start the air conditioner I might offer the following....
Look on the air conditioner product label and you will find information concerning the supply voltage and current. This is a 2 ton unit and it probably requires 220VAC power. Also on the label will be a value for the maximum OPD (over current protection device). This indicates the maximum fuse or circuit breaker that can be installed in the power feeder line for the air conditioner. You will need a generator that is capable of supplying this amount of current during the start up of the air conditioner. The value is usually about 2-1/2 times the normal operating current that the generator will need to supply continuously. This is because the air conditioner is full of motors that draw a lot of current when starting up. If the generator can't supply sufficient start up current, the motors will not start and the AC will not operate. As a result, the generator size is usually relatively large in comparison to the actual size required to keep the AC running after start up. This is also why AC units are not typically powered from generator power. Good Luck!
Without looking up the specifications for this heat pump, I cannot be certain, but I expect the operation to provide cooling may require more power than when heating. You probably can find the specifications online for this unit. As you probably know, power is measured in watts and is calculated by voltage times current. This also is likely to be 240 volts operation. If you take the specified power on cooling and divide by voltage (240), that will indicate the current in amperage that will be required to start it. Your circuit breaker is set for current and needs to be a higher current than is required. If that is the problem, you can buy circuit breakers at Home Depot or Lowes. You have to remove the front panel of your breaker box and snap out the circuit breaker. To be safe it would be good to turn off the main breaker switch before you open the front panel and remove the circuit breaker for the heat pump. Should your calculation of current required be less than the rating of the circuit breaker, that implies a malfunction of the heat pump in the cooling mode and would require a service call to the local representative of the heat pump manufacturer.
Your question needs more detail. The term "contacts" refers to the size of switch components and have nothing to do with the amount of current they will carry. Watts is calculated by voltage times current in amperes, or amps. If your AC is running on 110Volts, then 40-watt contacts would be able to carry about .0.4 amps. That does not sound sufficient for an air conditioner, so more clarification is needed. I would expect an air conditioner to require more like 400 watts to operate.
Consider the power consumption and Voltage of Air conditioner . Why you might ask because you can calculate likely current requirement. Power = Voltage x Current. So Current = Power / Voltage. Eg a 4800 Watt power on say a 240 Volt supply. Current calculation 4800/240 = 20 amps. As a rough guide what fuse rating is the fuse in the fuse box of the house for the AC power point. I would think 15 amp for lighting and between 20 Amp to 30 A for power.
Most likely the air conditioner draws more power than the generator can supply. Check the current needed for the air conditioner in amps. It should be on a plate attached to the it. If the generator is a 5000 watt it can supply 5000 divided by the voltage required by the airconditioner. i.e. 240 (=20.8 amps) if you live in the UK or Ireland or 120 (41.6 amps) in most of the rest of the world. If it's a 12 Volt Airconditioner than you divide 5000 by 12 Note this is the absolute maximum that can be drawn and as power generally fluctuates will still probably cause the circuit breaker to trip. You should ideally be drawing no more than three quarters of the current available. If there are other appliances being run off the generator this again reduces the amount of current available.