# Work done by rolling vs skidding friction force

Two identical bicycles having equal weight riders are traveling along a level road adjacent to each other with the same non-zero velocity. Bike A, (the "skidder"), applies the rear brake strongly enough to lock up the rear wheel which begins to skid. Bike B, (the "roller"), also applies the rear brake, but not so strongly and in such a manner that the same frictional braking force is achieved at the rear wheel. Bike A and Bike B both slow at the same rate and come to a stop at the same time. The time spent and distance traveled as they slow to a stop is the same. The only difference is that Bike A skids to a stop with a locked up rear wheel and Bike B rolls to a stop without skidding at all.

For both of the following two questions, assume that there is zero friction in the bicycle drivetrains and zero air resistance and zero rolling resistance. Also, ignore the infinitesimal energy transferred from the bikes to the Earth.

1. Bike A (the "Skidder"): From the ground reference frame, does the (kinetic) skidding friction force of the road acting on the tire do any work on the bike as a whole?
2. Bike B (the "Roller"): From the ground reference frame, does the (static) rolling friction force of the road acting on the tire do any work on the bike as a whole?

My understanding is that the rolling friction force is constrained and can do no work on the wheel of the bike, but does it do work on the bike as a whole? And if so, how?

• why do you see a need to differentiate the wheel from the bike when they are attached by the axle? could you not have rephrased the question as Wheel A and Wheel B without any mention of bikes? – gregsan Dec 12 '13 at 19:33
• @gregsan - I understand that a static friction force does no work on the rolling wheel component of the bike - my question is does that force effectively do work on the machine as a whole - i.e. on the bike?. There is a difference. – ridgerunner Dec 12 '13 at 23:15
• then your question really is about rolling resistance, which emerges from deformation in the wheel (flattening at the contact area with the road) or deformation in the road or both. the result is the Normal force being off-perpendicular to the road and this have a horizontal component acting against the center of mass of the wheel/axle/bike. an infinitely rigid wheel and road will not have rolling resistance and will roll forever. – gregsan Dec 13 '13 at 7:11
• My question is not about rolling resistance - it is about the work done (or not done) on a whole machine taken as a single free-body, by a horizontal friction force acting from the ground in the frame of reference of the ground. I clearly state in the question that rolling resistance is to be ignored. – ridgerunner Dec 14 '13 at 15:14
• then it is obvious that your question is moot since you effectively ignored all forces of friction for a rolling wheel. if neither the ground nor wheel deforms then that is indication that there is no force opposing the relative motion of the ground and wheel/bike – gregsan Dec 15 '13 at 3:05