# A heat engine based on rubber bands

In Feynman's treatment of thermodynamics, The Laws of Thermodynamics, $$44–14$$ Heat engines; the first law, Feynman said we can use rubber bands to make a heat engine like the one below.

It consists of a bicycle wheel in which all the spokes are rubber bands. If one heats the rubber bands on one side of the wheel with a pair of heat lamps, they become “stronger” than the rubber bands on the other side. The center of gravity of the wheel will be pulled to one side, away from the bearing, so that the wheel turns. As it turns, cool rubber bands move toward the heat, and the heated bands move away from the heat and cool, so that the wheel turns slowly so long as the heat is applied.

Previously, he said rubber band contracts when heated. I think that's what he meant by stronger, but how does this explain the shifting of the center of mass from the bearing?

Contracted or not, the rubber band's mass stays the same, so each sector of the wheel containing a rubber band will have the same mass as before; thus the distribution of mass should be unaffected by the heating in one side, isn'it?

• Maybe because of length changes?? Dec 30, 2019 at 13:39
• He's a link to a cool demonstration, in case you haven't already seen it: youtu.be/dBXL93984cQ Dec 30, 2019 at 14:36
• I remember seeing one just like that in a display case in the science museum of the Franklin Institute when I was a kid. You pressed a big red button below the window to turn on the heat lamp, and some moments later, the wheel would slowly start to turn. I think they also had an opaque card in there to shield the "cold" side of the wheel from the rays of the heat lamp. Sad thing though is that I have no memory of what lesson I was supposed to take away from the demo other than maybe, "science is cool!" Dec 30, 2019 at 17:38
• @SolomonSlow if the only lesson you took was that science is cool, it was well worth it! Jan 1, 2020 at 13:55

## 2 Answers

Just to elaborate on @Adrian Howard answer, the heated rubber bands on the left side of the wheel contract, pulling the left side of the rim closer to the bearing and the right side moving further away from the bearing (assumes the rim is rigid and does not deform). In order for the rim to move to the right while the bearing remains in place, the cooler rubber bands on the right have to stretch. The net result is the center of mass of the wheel shifts to the right of the original center of mass.

The figures below may help to visualize what is happening.

The wheel at the top is not heated and therefore the center of mass of the wheel is at the center of the bearing.

The lower left figure shows the shift of the rim of the wheel to the right of the bearing due to the contraction of the rubber bands on the left (causing stretching of the rubber bands on the right).

The lower right figure shows how the shift in center of mass of the wheel to the right creates a clockwise torque about the bearing causing the wheel to rotate.

Hope this helps

• Hey, what did you use to draw those diagrams looks very clean. Mar 1, 2021 at 7:23
• @JustJohan I copied the OP image to a PowerPoint slide and added drawings to it. In order to post it in my answer, I had to convert (or export) the PowerPoint file as a JPEG file. You can drag and drop a JPEG file into your answer. Have fun! Mar 4, 2021 at 21:53

The hotter, tighter bands will pull the steel rim off center, so the rim will be pulled to the right in your diagram, making the right side heavier.

• Doesn’t this require the rubber bands in the upper left quadrant be hotter than the lower left for there to be a net clockwise torque on the wheel? Dec 30, 2019 at 14:22
• @BobD Yes, the diagram probably does not show optimal positioning of the heat sources. Dec 30, 2019 at 14:27
• Gravity provides the torque, from the center of mass shift. Dec 30, 2019 at 14:36
• Optimal performance would have the offset center of mass always directly horizontal to the axis, for greatest gravitational torque. Dec 30, 2019 at 14:39