I've just started playing the violin, and have come to dynamics (forte, piano, etc.). To play forte, I push the bow hard, and for piano, I push the bow lightly. Is this the right method? Are there any better methods?
The concept I was taught for violin dynamics is that you draw the bow faster across the strings to play more loudly, and slower to play quietly. You do have to apply more down pressure on the bow to keep it from skipping when you bow faster, and less down pressure when bowing slower, but I was told those are secondary concerns that arise from the speed of the bowing.
Considering how down pressure has to be continuously varied on the bow even when playing at a fixed speed, I find the mental attitude that bow speed is related to loudness is the sensible way to look at it.
In terms of the physics, it's at least a combination of bowing speed and pressure that changes the dynamics. From a playing perspective, I prefer to think of it as primarily bow speed with pressure being something I have to manage based on many other factors.
The main thing for a beginner is to play forte with longer bow strokes which is faster bow speed and piano with smaller bow strokes which means slower bow speed.
If the bow glides down towards the fingerboard especially on longer bow strokes it can be because your bow strokes are not straight. You need to practice straight bowing and be flexible in your right wrist. Also make sure that you hold the violin up. If the violin is "hanging" the bow can glide towards the fingerboard and you will often automaticcally try to prevent it with a harder grip on the bow which can make the tone quality less desirable. Straight bowing and a good violin hold supports a good violin tone.
There is lot more to bow technique, you will gradually learn more and more along your journey into the great realm of violin playing.