# Is the traditional free-body diagram invalid in situations in which equal forces produce unequal powers?

This question is in response to question B1 in the problems/solutions located at http://aapt.org/physicsteam/2013/upload/E3-1-7-solutions.pdf.

In question B1, there is a wind-powered vehicle that can travel both against the wind and with the wind, and in both cases potentially may go faster than the wind itself.

The force generated by the wind on the propeller is opposite but equal in magnitude to the force the wheel exerts on the ground. In a traditional free-body diagram, one would say the forces balance, therefore the velocity is constant. Moreover, there is loss due to friction and so presumably the vehicle would come to rest.

This, however, is not the case. In the against-wind case, the propellers move through more air than the wheels do ground. The propeller then produces more power than the wheels consume. As a result, the craft speeds up until the frictional loss and the wheels consume as much power as the propeller generates.

It would seem that there must be a restriction on free body diagrams that all forces act through the same distance - or something else of that nature. Is this correct? What restrictions must a free-body diagram have to be guaranteed to be accurate?

• See, the only restriction of a free body diagram is that the reference from which it is drawn, must be an inertial frame. Now what is the problem here? That we have to examine more carefully, and that's why I wrote this in comments. But take my word for it, the FBD is accurate if the frame is isolated. Commented Jul 28, 2013 at 16:45
• @SaurabhRaje I think the frame is still considered inertial, but different parts of the body pass through different distances in their respective media. Commented Jul 29, 2013 at 17:18
• So, that means the FBD must be drawn for a wheel, or propellor? ? Commented Jul 31, 2013 at 4:54
• @SaurabhRaje The FBD is drawn for the craft as a whole has a force on the propeller and a frictional force on the ground. The propeller's FBD consists of a input force from the wind and then some sort of output force on the wheels such that the wheels receives less power than the wind put in. Commented Aug 1, 2013 at 2:17