I would like to determine the weight capacity of a cabinet made of 1/2" plywood which is 18" deep and 60" long, 37" high.
The cabinet has 2 sides and 2 uprights spaced about 20" from either end. The top is also 1/2" plywood.
Given the information offered the only way to arrive at an answer is (as mentioned in the comments) to experiment with different weights and see what works.
Big Bang Method
If over loading the cabinet will not cause a catastrophic event - hurting someone or damaging something you care about - you could load a large amount of weight and then periodically observe the cabinet for bending / breakage. Let the weight sit for some period of time and check again. Personally, this method makes me nervous.
Slow but Steady Method
A more cautious method would be to start with low weight items - observe over a period of time (say once each hour for example) and increase the weight a little - observe and repeat until the ideal weight is found.
Be sure to identify the part of the cabinet that connects to your house. If the cabinet sits on the floor you will want to observe the parts of the cabinet that transfer the contained weight to the floor. If the cabinet is mounted to the wall you will want to observe the wall mounts.
One way to go at it would be to determine how much weight you need it to hold.
If you only need it to hold a few pounds the materials in the cabinet can handle that as long as the weight in the cabinet is transferred well to the house (floor or wall).
If you need it to hold as much weight as you can stuff in then do some testing.
Try the sagulator. While I wouldn't hang my hat on it as, jdv mentioned, each piece of ply will be different, it'll give you an idea if the weight you want to put on it is in range or not. https://www.woodbin.com/calcs/sagulator/
If your wall studs are 16" on center, 64" equals 4 studs on center. A 66" cabinet would allow for a pattern of 4 screws per row, with a total of 3 screws at 6" spacing for up and down rows. Using 3" stainless wood screws, with a 60" cabinet you would only hit 3 studs at 16" O.C. (16", 32", 48") you would want to open the wall to add support backing, with whatever material your wall studs are, patch the walls up, or using wall anchors (which I don't recommend for this project). Hope this helps/