
OH, LORDY

..........
Sorry Physics is my thing, and passion. There is some good and some bad physics in this thread. I have pushed the pencil through MANY similar problems. I will do my best to set some things straight.
Physics Forum, Wikipedia, etc. often will give you the wrong/incomplete information. Earlier in the thread Mu sub S, and Mu sub K were given for static and kinetic(moving) friction calculations. If you analyze these, (not directly applicable),calculations you will find Mu sub S is NOT dependant upon surface area contact. WOW!! , this means a glass setting on the small surface area rim, has the same friction as when it sets on it's (large surface area base).
This means a dragster would have the same traction with bicycle tires, why do we bother putting these crazy wide slicks on the back!
Because Drag racers know better, ALL general Mu sub S and Mu sub K friction calculations ASSUME surfaces are (Perfectly flat) 2 dimensional surfaces. This works pretty well with the smooth glass on the formica countertop. BUT, real world tires are VERY different and VERY 3 dimensional in surface contact,(shearing forces must now be taken into account). That's why these equations,(without modification), dont work for this application.
Back to the original question.........
It is a
TRICK QUESTION, what we are talking about is a moving object that we alter with a passenger, (increasing mass). The Bottom line initially is about conversion of kinetic energy to thermal energy. We increase kinetic energy by increasing the bike's effective mass. Formula for Kinetic Energy is 1/2 Mass times the Velocity squared.
The good news is that when we look at (K.E. = 1/2M x V^2) is that the 1/2 in front of the Mass is, (from a math perspective), not very powerful. We can increase the mass some and not have a profound effect. The other side of the coin is the squared term on the Velocity, a small increase in velocity has serious kinetic energy influence.
Blah Blah Blah.....now for the conclusion
DONT SPEED WITH A HEAVY PASSENGER ON YOUR BIKE
The passenger has INCREASED kinetic energy, (some passengers increase more than others

). This increase in kinetic energy must be thermally dissapated through the brakes, tires, etc.
Does this mean more stopping distance? maybe/maybe not. Extra effort WILL be needed to keep the same stopping distance BUT, if you dont exceed capability of brakes/tires you CAN stop in the same distance.
(Yes Mu sub S and shearing forces will increase some from the added weight, this seemingly simple problem is actually very complex).
The problem varies even more with added Velocity, that increase in mass,(passenger), makes things FAR worse at higher speeds.
Hopefully this clears some things up, pm me if you have questions. Sorry if I rant when it comes to Physics(or bad Physics). Yep, I'm a nerd.

eace:
If your still bored try to answer this one:
I have seen shock sensors (little sand filled simple mechanical devices) on the outside of some shock sensitive containers (packages). These can be purchased in various "G" ratings. Lets say I have a shock sensitive package(5 lbs.) and I drop it from my waist to the concrete floor, (3 feet), how many g's will show on my indicator?