How Much Weight Can A 4x4 Post Support How Much Weight Can A 4' Horizontal 1.5" Poplar Dowel Attached To 4x4 Posts Via 3" Deep Holes Safely Support?

How much weight can a 4' horizontal 1.5" poplar dowel attached to 4x4 posts via 3" deep holes safely support? - how much weight can a 4x4 post support

I am building a bar, outdoor games for my daughter of the species (as) playgrounds, and was under the impression that a piece of wood would be about 1.5 cm thick enough to hold (weight approx. 60 pounds) but now I'm afraid, if more than one child climbing (ie) a total of perhaps 120 pounds, breaking it. The wood is poplar. I do not want anyone to get Impaled!