碰 has both physical (to bump/touch) and figurative (to encounter) meanings. 碰杯 means "to clink glasses" for a toast. 碰钉子 (to hit a nail) means to be rejected or rebuffed.
Left indexing stone radical — depicts a rock fallen from a cliff (厂 cliff over 口 stone-piece). Carries the meaning of solid impact: bumping is rock striking rock. The radical anchors 碰 in the stone family with 砸 smash, 破 break, 硬 hard, 砍 chop.
phonetic
並bìng
side by side (here phonetic)
Right 並 supplies the sound (bìng → pèng through b/p alternation). 並 itself depicts two figures standing shoulder to shoulder, lending a faint semantic flavor: two things coming side by side until they touch — the moment of the bump. A relatively late character (post-Tang) compared to most phono-semantic compounds.