Galileo's Experiments

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 toquestions 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 didnít 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 doesnít work.

 

 

 

III. Inclined Plane Projectile Motion

 

Background sites

PBS site††††† Description of experiment with images of G.ís 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

 

  1. 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.
  2. 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?