I agree that when it is possible to make measurements on-site projects tend to be seen as "make
work" and not too interesting. If the building has been completed (or not) you could send a student
to the top floor to throw something out a window. Something white and shiny. At bottom you set up
several cameras with the purpose of photographing the falling object just as it is about to hit the
ground. Set up a nice black background to photograph against and include a ruler next to the impact
zone. The ruler will allow you to make measurements. Of what you ask? Of the length of the blurred
falling object. Use a 1/100 second exposure time if you have it or anything like that. Make a
picture of the object before it is thrown out the window and standing still in same area as you
expect impact to happen.
So now you have two pictures. One of still object and another of the blurred one. Measure them using
the ruler included in the scene. Then take the size of the object and subtract it from the size of
the blurred image. The difference is approximately the distance the object fell during the time the
shutter was open. Dividing that distance by the exposure time gives you the speed or velocity of the
falling object.
Once you know this you can work backwards to find out the height from which the object was released
based on acceleration due to gravity. I think one expression for this goes like: Velocity squared =
2 times A times the distance fallen. Where A = acceleration due to gravity = 32 feet/sec/sec.
Another way to express the same thing is Distance Fallen = Velocity Squared divided by 2A (or 64)
Since you know the velocity of the object (from 2nd paragraph above) you multiply it by itself and
divide that by 2 x 32 or 64 and you determine the distance from the ground to the drop zone.
Roughly. Then you can drop a string from the window and measure its length to compare calculated
distance vs. length of string distance.
For example, if you determine that the object produced a blur of about 6 inches at an exposure time
of 1/100 second then it was moving at 6" / 1/100 sec or 600 inches per second and that is 50 feet
per second. OK - now 50 x 50 = 2500. That divided by 62 = 39 feet - thus the object was released
from 39 feet above the ground. Roughly. The same with metric but blur measurement would be in meters
and A = 9.8 - so 2A = 19.6
Depending on what you throw out the window could make this a memorable event!!
andy
PS: I hope the above is correct and if not please provide corrected version! Of course it does not
take air resistance and a couple of other minor factors into account.
David Dyer-Bennet wrote:
However, it's easy enough to go in with a tape measure to your own
library; makes this an obviously-artificial exercise, which aren't the
best for motivating students.
