Due in class (10 AM) on Friday, March 14.
- Assignment 6 on our MasteringPhysics course site.
- Y&F end of chapter problems.
- 1.55.
- 1.90. Solve this using the dot product, not by using geometry. You would use a similar procedure if, for instance, you needed to calculate bond angles using the positions of atoms in a protein. This type of problem comes up frequently in structural biology when converting from a PDB file (essentially a list of position vectors) to bond lengths and angles.
- 6.3.
- 6.48.
- 6.67.
- 6.82.
- The plot to the right (click on it to enlarge / save to disk), which was taken from Steven Vogel's book Comparative Biomechanics, shows the energy expended by a person (J) per mass of the human (kg-1) per distance walked (m-1) for a person walking up or down slopes of various steepness (aka grade). Based on the physics alone, it should require energy / meter to walk uphill (against gravity), no energy to walk on flat land, and we should pick up energy when moving downhill (with gravity). This is what we would observe if we had frictionless wheels instead of legs. In fact, physics prescribes a lower limit of the amount of energy required to move. Since our bodies are not perfectly efficient, in reality we require extra energy above the theoretical minimum. I want you to calculate this "extra" energy, which one could plausibly call the physiological inefficiency.
Derive a (simple) formula for theoretical minimum energy cost per kg per m moved.
Print out the plot of observed efficiencies and add a line showing this theoretical minimum.
- Graphically, find the part of the walking graph with the least physiological inefficiency. Note that this is not the bottom of the walking cost curve.
- Describe how to locate (graphically) the point with the smallest inefficiency.
- What grade (in degrees) is least inefficient?
- What is the extra cost (in J/kg.m) on that optimum grade? This is the premium that we pay for the privilege of having legs.
