Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: acceleration



Harry asked:
Our quiz bowl coach would like to know the appropriate response to
the following question. What is given by the first derivative of
acceleration?

It is clear to me that Harry was thinking about the derivative with
respect to time. My answer --> The first derivative shows, in case of
a vertically falling styrofoam ball (a parallel thread), how the air
resistance force depends on velocity.

It occured to me that data can also be collected with a helium balloon.
Attach a small nut and measure terminal velocity. Attach two nuts and
measure an increased terminal velocity, etc.

Here are some fake data (from a simulation with Interactive Physics
using its default air resistance). The sphere diameter was 20 cm

mass= 50 grams v_term=0.49 m/s after dist=0.18 m (t>0.4 s)
mass=100 0.98 0.60 0.7
mass=150 1.47 1.25 1.0
mass=200 1.96 2.31 1.4
mass=250 2.49 3.87 1.8
mass=300 2.94 5.79 2.9

I do not recall how air resistance is calculated for a "round object"
in IP. Do they assume it is sphere? Or a cylinder of unit length?

For each mass I have v(t) which becomes a constant value after the time
interval shown in the last column. A camcorder will collect real data
and students may be challenged with calculating the derivative of the
acceleration, the derivative of that derivative, etc. Yes, with respect
to time, or with respect to distance, if you wish.
Ludwik Kowalski