Read the second chapter of Nonsense on Stilts (Pigliucci) and write a one-page reaction to or summary of.
Due: Sept. 8
Monday:
Labor Day
Wednesday:
We returned to the idea of simple machines and mechanical advantage. I corrected my earlier mistake that a wheel (and axle) can
be used as simple machine if the wheel supports multiple radii. Then one could apply a force at one radius and achieve the
effect on a different force at another radius of the same wheel.
In discussing mechanical advantage we often considered overcoming some weight. So we discussed in some detail what weight is
and what it depends on. (The distinction between mass and weight is important in physics.) What we typically mean by weight
is the gravitational attraction between an object and the Earth. Though we can talk about the weight of something on the Moon.
We said that the weight can be expressed by the formula W = m g, that is, the weight is the mass of the object (which we will
take to be measured in kilograms) multiplied by the acceleration due to gravity (which we will take to be 9.8 m/s2
on the surface of the Earth). The g as we will see later depends on the mass of the Earth and the radius of the Earth.
Given that the force that we are often trying to overcome with a lever is an object's weight which is its attraction to the
Earth, this makes Archimedes supposed statement "Give me a lever long enough and a fulcrum on which to place it, and I shall
move the world" a bit weird. We could conjecture that it is some other gravitational force, say the Earth's gravitational
attraction to the Sun that one is overcoming.
We decided to talk about an ideal lever arm (massless) -- that way we did not have to worry about the weight of the lever arm.
We noted that the larger r (the lever arm -- the distance from the applied force to the fulcrum) the smaller the applied force F
had to be to overcome the weight of the object m g. At this stage we would say that the variables F and r have a "negative
correlation". We next attempted to come up with a formula for the realtionship. Toward this end we considered a process known as
"dimensional analysis" that says that the two sides of an equation should have the same units (dimensions). We finally
came up with
F = m g d / r = m g d r-1
Another way to write a formula with the variable r in the denominator is to write r raised to the power of -1. That makes
this formula to fall into the category known as Power Laws. The specific power of -1 is also called an inverse or
reciprocal relationship.
