Is there a way to update my 40GB Playstation 3 so that it can play playstation 2 games?

May be...

No.

It is not possible to run PS2 games on the 40GB PS3.



The original playstation 3's (20GB and 60GB) actually had the PS2 EE+GS chip in them ("Emotion Engine" = CPU, "Graphics Synthesizer" = GPU). This gave them compatibility of between 95-98%, some games still have some issues, mostly due to I/O devices (controllers, Network etc.)



For the 80GB version sony replaced the PS2 chip with one that just had the Graphics Synthesizer. The Emotion Engine was emulated with software instead. This resulted in a compatibility of about 80%, though as it is software, it can be updated, and the number of compatible games has grown with each release.



To save costs on the 40GB system the chip containing the GS hardware was removed. This means there is no longer any PS2 hardware. The PS2 functionality cannot be achieved with just emulation, the emulator would need customizing for each game, and Sony have already said they are focusing on the PS3's future, not backwards compatibility.

you cant update it, its in the hardware. thats the main problem with the 40 gig ps3