Galileo Projectile Motion Experiment

Student Instructions

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.

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:

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?

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. What determines how far the ball travels before it hits the ground? Galileo also discovered a mathematical answer to this question.

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.

Horizontal distance	1 unit	2	3	4	5	6
Trial 1 distance
Trial 2 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.

Vertical distance	1 unit	2	3	4	5
Trial 1 distance
Trial 2 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?