They move quickly when disturbed and they tend to have some silk or web attached to their body and when you pulled the cooler away or lift a log it yanks the spider in that direction giving the appearance that it jumped towards you.
Do Black Widow Spiders Jump?
From what I read they don't jump, but some species of spiders can jump but no spider intentionally jumps at people.
www.kamalii.k12.hi.us
www.calpoison.org
www.kamalii.k12.hi.us
www.calpoison.org
Not that I know of but I can't tell you for certain. Everytime I see one it looks really lazy in the corner.