# Dynamics

Now that we have completely described your fall from the roof and subsequent collision with the ground, we are ready to ask two more sophisticated questions: why did you fall in the first place, and why did it hurt when you stopped?

W = m g.
When we speak of inertial mass, we mean the mass which determines how much acceleration you experience under the influence of a given force, as given by Newton's Law:
F = m a.
While there is no conceptual reason why these two masses should be numerically equal, they are. This is one of the fundamental mysteries of physics.

### Elasticity and Strength

Shear is a distinct possibility in a fall, but it is so difficult to handle mathematically that we will restrict ourselves to a discussion of breakage by compression.

• k = kilo ( 10 3 )
• M = mega ( 10 6 )
• G = giga ( 10 9 )
• T = tera ( 10 12 )
• c = centi ( 10 -2 )
• m = milli ( 10 -3 )
• μ = micro ( 10 -6 )
• n = nano ( 10 -9 )
• p = pico ( 10 -12 )

Typical values for some types of human bones are:

bonecompressive strength (MPa)
femur (upper leg)167
humerus (upper arm)132
tibia (shin)159
cervical vertebrae (neck)10
lumbar vertebrae (lower back)5

So we see that we need two additional pieces of information in order to find out how badly you were hurt: the compressive strength of the bone which took the impact (we will assume that a single bone took all of the impact), and the size of the area which hit the ground. Knowing the force and surface area of the impact, we can compute the pressure which was applied to the bone, and compare that to the strength of the bone to determine the extent of the damage.

The following applet builds from the one in the last section. Decide which bone took the impact and compare your answer for the pressure to the table above to decide if you are headed back up the ladder or to the hospital!

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download the Java VM (Virtual Machine) for your version of Windows at the download section at java.sun.com.

The next section discusses two fundamental conservation principles which lie at the very heart of physics.