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.
- 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?
- 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?