I yearn for practical scientific knowledge. Unfortunately, I have come upon no practical scientists, so I turn to you, Cece. What makes Scotch tape stick? Also, why can't you light a match on sandpaper, but you can on the strip of flint provided on the matchbook?
Unfortunately, it seems that nobody quite knows what makes tape–or any other sort of adhesive–stick. Most tapes are made with synthetic elastomers, which are very long molecule chains (polymers) that have certain elastic properties. Up until the 1960s, it was assumed that sticking was either a mechanical operation, involving the dovetailing or interlocking of molecular structures, or a chemical change that formed new chemical bonds.
Now there is a theory of adsorption that postulates adhesion to be a result of the universal property of attraction that holds all matter together. Presumably, if this hypothesis is correct (and it appears to be enjoying some popularity), than any two materials will adhere if jammed close enough together.
As for your second question, one of the combustion elements that sets safety matches off is red phosphorous, which is contained not in the match, but in the "strip of flint." Without the red phosphorous, it takes more friction than most mortals can produce to get a rise out of the match head, which characteristically contains antimony sulfide, an oxidizing agent such as potassium chlorate, and sulfur or charcoal. In most wooden matches, by contrast, which usually you can light on sandpaper, everything you need to get things cooking is contained in the matchhead.
Send questions to Cecil via firstname.lastname@example.org.