Stopping Speed and Distance
Date: 08/28/2001 at 20:43:01 From: Adam Seaberg Subject: an 18 wheeler vs. a motorcycle in stopping t school today I was asked the question "out of a 18-wheel tractor- trailer and a 2-wheel motorcycle, which would be able to stop faster or in a shorter distance? I responded with the 18-wheeler because it has more cubic sq. in. of rubber on the ground compared to weight or mass than a motorcycle does. I was told that I was wrong but I don't believe it, so I decided to go to someone who would help me prove it. I feel that this is a very very interesting question and I would really appreciate your help on this Thank you, Adam Seaberg
Date: 08/29/2001 at 14:26:46 From: Doctor Rick Subject: Re: an 18 wheeler vs. a motorcycle in stopping Hi, Adam. Yes, it's an interesting question. My first guess is the opposite of yours. My brother has driven fairly large trucks, and he complains about people who pull in front of him while approaching a red light. He says people don't realize that a truck has a longer stopping distance. Let's consider the physics of stopping. A moving vehicle has kinetic energy equal to half the mass times the velocity squared. If the truck and motorcycle are moving at the same speed, their kinetic energies are thus proportional to their masses. If a constant stopping force is applied to a vehicle, the energy dissipated is equal to the force times the distance. The kinetic energy goes to zero (the vehicle stops) in a distance such that the force times the distance equals the kinetic energy. The stopping distance is thus the kinetic energy divided by the stopping force. The maximum stopping force that can be applied without skidding is equal to the normal force (the force with which the vehicle is pulled against the road) times the coefficient of static friction for the tires on the road. If we assume that the truck tires and motorcycle tires have the same coefficient of static friction, then the maximum stopping force is proportional to the normal force, which is proportional to the mass. Why doesn't the stopping force depend on the number of tires? The weight of the vehicle is distributed among the tires. If you double the number of tires, you halve the average weight supported by each tire. The maximum stopping force is proportional to the weight supported by the tire; thus the stopping force from each tire is halved. Half the force from twice as many tires means the same total stopping force, independent of the number of tires. The stopping distance is proportional to the kinetic energy divided by the stopping force, and each of these is proportional to the mass, so this proportionality cancels out. The stopping distance, according to my reasoning, is independent of the mass of the vehicle; it should be about the same for a motorcycle or a tractor-trailer. Does this mean we were both wrong? I do find it surprising - it goes against what I had always assumed - so I checked on the Web and I found this site that supports my reasoning: Stopping Distance for Auto - Dr. Rod Nave, HyperPhysics, Georgia State University http://hyperphysics.phy-astr.gsu.edu/hbase/crstp.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.