In-Lever, Out-Lever (Station 8)
by Greg Crowther
This song, written for BBIO 352 (Principles of Anatomy & Physiology II), addresses two common problems that arise in applying the physics of levers to biomechanics.
First, some students have trouble remembering that the mechanical advantage equals the in-lever distance Li ("L-sub-i") divided by the out-lever distance Lo ("L-sub-o"), so the song provides that formula.
Second, some students struggle to measure Li because they think of it as "the distance from the fulcrum to the muscle," which is ambiguous. Which PART of the muscle should we measure to? The lyrics remind us that Li is from the fulcrum to the muscle's INSERTION (usually via a tendon) onto the lever (usually a bone).
This song is subtitled "Station 8" because it was originally conceived as one station of a lab exercise in which students rotate among several skeleton-related stations.
In-lever, out-lever, in-lever, out.
How do you amplify a whisper to a shout?
Make the mechanical advantage extra-stout:
Elongate the in-lever; shorten up the out.
L-sub-i is fulcrum to insertion of the muscle;
L-sub-o is fulcrum to location of the load.
Finding the mechanical advantage is no puzzle:
Just take the L-sub-i and divide by L-sub-o.
• MP3 (demo)
• music video
• sheet music (with melody play-back)
Songs like this one can be used during class meetings and/or in homework assignments. Either way, the song will be most impactful if students DO something with it, as opposed to just listening.
An initial, simple follow-up activity could be to answer the study questions below. A more extensive interaction with the song might entail (A) learning to sing it, using an audio file and/or sheet music as a guide, and/or (B) designing kinesthetic movements ("dance moves") to embody it. The latter activity could begin with students identifying the most important or most challenging content of the song, and deciding how to illustrate that particular content.
(1) What units does the mechanical advantage have?
(2) What range of values can a mechanical advantage have?
(3) Mechanical Advantage can also be calculated from the force in (Fi) and force out (Fo), or from the velocity in (Vi) and velocity out (Vo). How do those formulas compare to the one presented in the jingle?
(4) Your calf muscles (gastrocemius and soleus) attach to your heel via the Achilles tendon. Where is the fulcrum for the movement of extending your foot? Is the mechanical advantage of the calf muscles greater than 1 or less than 1?
(5) How does "amplify a whisper to a shout" fit into this song? Do the bones of the middle ear use levers and mechanical advantages to amplify sounds?
(6) While individuals cannot adjust the mechanical advantages of their anatomy, evolution CAN select for low or high mechanical advantages. Consider the armadillo's forelimbs, used for digging, and the cat's forelimbs, used for running. Which animal's teres major muscle, whose origin is on the scapula, should have its insertion on the humerus closer to the shoulder joint? Why?
(Answers may be found on the answers page.)