This is a Chain Fruit or Hanging Chain Cholla. It and its close cousin (also here), the Teddy Bear Cholla are both also referred to as "Jumping Cholla". The earned that nickname as it appears that small pieces seem to jump onto you by just walking near them. What typically actually happens is that you step on a small piece that is on the ground. Then as that foot move up and forward while walking, it can hook onto the back of your calf. Also, any slight brushing of the plant by your clothing will result in small branch segments sticking to you. The spines are extremely sharp and have microscopic barbs on them that imbed in your clothing and you, making them hard to remove! When hiking in areas with these, it is a good idea to carry a comb and a pair of needle nose pliers. The comb can be used to remove a branch segment, and then the pliers to remove spines that remain in you!