Galileo Seminar 4
Demonstration Instructions
I. Pendulum and Free Fall Experiments:
Instructions for No Measurement Version
Instructions for full
experiments with quantitative measurements
Pendulum Experiments:
Student Instructions and Datasheet
for full experiment. (to Print for distribution to
students)
II. Inclined Plane Rate of Acceleration:
"...in such a plane, just as well as in a vertical plane, one may
discover how bodies of different weight behave..." Galileo
When Galileo caused balls, the weights of which he had himself
previously determined, to roll down an inclined plane; . . .a
light broke upon all students of nature. They learned that reason has insight
only into that which it produces after a plan of its own, and that it must not
allow itself to be kept, as it were, in nature's leading-strings, but must
itself force . . .nature to give answer to
questions of reason's own determining. Immanuel
Kant, Critique of
Pure Reason
Background Sites:
Galileo
Project Inclined Plane experiment PBS site on
Inclined Plane Art of Rennaisance Science Inclined Plane Analysis
In this Demonstration Galileo arrived at his law that the
time is proportional to the square of the distance traveled.
Student Instructions and
Datasheet
Preliminaries:
Drop a few balls and see how they speed up as they fall further
and further. Now let some balls roll down the ramp and note how their speed
changes as they get further down the ramp.
Why do you think Galileo used the ramp to measure the rate instead of
dropping objects? Why do you think rolling balls down a
inclined plane tells us something about how objects fall?
A. Measuring the Rate of Acceleration, Method 1: Video Instructions
In this method you will measure the distance traveled by the
ball by marking the position of the ball at equal intervals as measured by a
pendulum. Can you think of any other way
of measuring equal intervals. Galileo used his
heartbeat and a water clock, as well as a pendulum?
(see Student Instructions and Datasheet for
detailed instructions)
B. Measuring the rate of Acceleration, Method 2: Video Instructions
In this method people will call out as the ball passes them
and you will try to arrange the people so they call out in a regular pattern
with equal periods of time between them. Galileo knew from his music studies
that human can recognize deviations from a pattern up 1/64th of a
second.
(see Student Instructions
and Datasheet for detailed instructions)
Try this link from the PBS Tower
of Pisa site to see if you can figure out the right arrangement of
students.
Here is an image of an inclined
Plane with movable bells that was used for the same experiment.
C. Comparing different weights:
Video Instructions
Galileo tried this method but found it didn’t work as well
as the pendulum for proving that different weights fall at the same rate. It is
instructive to get your students to figure out why it doesn’t work.
III. Inclined Plane Projectile Motion
Background sites
PBS site Description of
experiment with images of G.’s notes. Galileo
Project Projectile Motion site
Our Galileo unit
page has several links to projectile motion simulators
This
site provides a simple explanation of what is meant by parabolic motion
Kids
site on the mathematics of the parabola
Galileo used an inclined plane to study the motion of
projectiles as well. He used the inclined pane to vary the speed of the object,
by starting it at different heights. He discovered not only the parabolic path
of all projectile motion, but also the mathematical law that governs the
relationship between the starting point on the ramp and the distance traveled.
Student Instructions and Datasheet
Set up: The inclined pane should be set up on a table
with the end of the plane near the end of the table so the ball can roll off.
It should be set up much higher (at a greater pitch or angle) than in the
acceleration experiment. You should attach the metal shunt to the nail at the
end of the ramp and line up the end of the shunt with the end of the table. The
shunt makes sure that the ball is traveling horizontally when it starts to
drop, rather than pointed down at the angle of the ramp. (See the Video Instructions for
how to attach the shunt.)
Preliminaries:
1. Vertical and Horizontal
motions are independent.
First have a student stand at
the end of the ramp holding a ball identical to the one being rolled down. Have
another student release the ball from the top of the ramp. The first student
will release that ball from exactly the height of the table at exactly when
they see the ball on the ramp reach the end of the table. You may have to try a
couple times to get the release point right.
The two balls will fall
exactly the distance, though one will be moving horizontally as well. Listen
for the sound as they hit the floor. Do they hit together? What does this show?
Why is it important?
A. Seeing the shape of parabolic motion:
Video Instructions
1. Use some of the plastic
balls provided and have the students throw them back and forth. Note the shape
of the balls path. If the students toss it back and forth at the same angle and
speed you should get a good view of the path as the ball traces it back and
forth. Try changing the angle you throw
it at. Try changing the speed of the throw. How does the path change? What do
all paths have in common? Can you figure out why they are all called parabolas?
Use this Golf range applet to try out
different angles.
2. Line up as many balls as you
can at the top of the ramp and have one student release them one after another
as fast as they can. Have the rest of the students kneel down and watch the
shape of the path the balls take. Try it again starting the balls further down
the ramp. Does the shape of the path change? How are these paths similar to the
ones you saw throwing the balls? How are they different?
Galileo traced out the path
by letting the balls fall onto a moveable platform and raising the platform
little by little and marking where the ball hit at higher and higher planes.
Can you think of any other way he could have measured the path given his
available technology.
B. Measuring the Distances.
Video Instructions
- Have a student mark where the ball hits each time
you let it go. Use your string to measure put one horizontal unit from the
end and let the ball go from there and mark where it hits. Now drop the
ball from two units from the end, and then three, and then four until you
get to the top of the ramp. Mark where each ball hits and measure the
distance.
- Now repeat same process, this time measure the
vertical distance up the ramp. First start the ball at the point on the
ramp one unit above the table. Remember that your unit is arbitrary and
measured with the string. Start with a fairly small unit (6 inches or so)
Then find the spot that it two units above the table and so on. Again,
mark where each ball hits and measure the distance.
Compare how the distance changes
with horizontal distance with how it changes with vertical distance? Which of
these is the better measurement or experiment? How can you decide? Galileo
discovered that the distance varies with the square of the height. Did you get
that result? How did Galileo know which
measurement was the important one?