Galileo Galilei

  1. Introduction

    Galileo performed some of the early, classic experiments on falling objects. He developed an innovative approach to measuring the speed of falling objects and we will duplicate that approach in this session.

  2. Objectives

    Our goal is for the students to discover that the distance that a falling object travels is proportional to the square of the time.

  3. Materials
  4. Vocabulary
  5. Presentation

    It might be very effective for the instructor to come to class as Galileo, in costume and with an age appropriate beard. Here are some paintings of Galileo.

    Portrait of Galileo as a young man. Portrait of Galileo as a middle aged man. Portrait of Galileo as a mature man. Portrait of Galileo as a working man. Portrait of Galileo as a old man.

    The University of Padova in Italy keeps Galileo's lecture room as he used it between 1592 and 1610 (almost exactly 400 year ago.) The room has a high lecture platform, much like a pulpit, and the platform where Galileo lectured is more than one meter above the floor. So if you really get into the act, find or build a platform like his.

    Galileo had such an interesting life. The instructor should read a few highlight of his life, possibly in that paragon of accuracy, Wikipedia. Then, during class time, the instructor can tell some stories in the "first person".

    Have the students duplicate Galileo's experiment with a ball rolling down a trough. An easy way to do it is to put one end of the 2X4 trough on the pad and then raise the other end a 10 cm or so. Then run two strips of masking tape down the outside of the trough, one on each side. Start the clock and with the students lined up on either side of the trough, have one student release a ball after a countdown (with the clock) to exactly 0. Continue counting up. Each student is assigned a number and when the count gets to the students' number, s/he marks the position of the ball by gently touching (and holding) the masking tape at the position of the ball. After the ball has reached the end of the trough, each student should mark the masking tape at their finger position with a pen or some sort of durable marker. Also, at some point, the student should write their assigned number by their marks on the tape. Repeat this operation several times (using the same ball) to find an average position.

    There are several options at this point. The students may want to use balls of different mass to see if the mass changes the speed of the ball. They may want to raise the end of the trough in 10 cm increments and see if that changes the speed of the ball.

    After each set of averaged runs, plot the average position of the ball as a function of time. If the class has time, encourage the students to develop a set of mathematical expressions that describe the speed of the ball as a function of mass and the height of the raised end of the trough.

    In the context of the scientific method, the students should develop a conjecture about the things they observed and think of some experiments the test those conjectures. The next few sessions will be devoted to experiments designed to evoke Newton's laws, so the class sessions will suggest the experiments.

    Some theoretical notes. The time for a ball to travel 7 m when one of end of the trough is 10 cm above the other end is about 11 seconds. When the end is raised 20 cm, the travel time drops to less than 8 seconds and at 30 cm the time is just over 6 seconds. Don't raise the trough too high because the points get difficult to measure and there are very few points.

  6. Evaluation