Page 8 - GALIET PHYSICS BLOSSOMS II+

(1) Space, Time, Mass, and Force: The ideas we have of space and time, of inertial and gravitational mass, and of the concept of ’force’, were first clearly formulated by Galileo and Newton.
(i) Describe how Galileo measured the way in which balls rolled down inclined planes. What measurements did he make, how did he make them, and what results did he find? To make these measurements, Galileo had to define both distance and time, and also measure distance and time intervals. Explain how he did this.
GALILEO
To determine the acceleration of a ball as it moved down a plane, Galileo experimented with an inclined plane consisting of a simple 7m long by 30cm wide by 5 cms. thick board with a smooth groove down in which he rolled a small bronze ball repeatedly to measure time as accurately as possible, in fact, so accurate that “the deviation between any two observations never exceeded one tenth of a pulse-beat...”1
What Measurements did Galileo Make?
To measure the dynamics of projectile motion, Galileo modified the inclined plane apparatus slightly. Galileo added to it a curved piece at the bottom, which deflected an inked bronze ball into a horizontal direction. The accelerated ball rolled along a flat table with uniform motion, and then fell off the edge. Where it hit the floor, it left a small mark. The mark allowed both the horizontal and vertical distances travelled by the ball, whilst in the air, to be measured. By varying the ball’s horizontal velocity and vertical drop, Galileo was able to demonstrate the parabolic motion of projectiles, doing away with the following Aristotelian projectile motion theories:
• Aristotle’s theory stated that an external force transmitted through the air moved projectiles. Because Aristotle could not conceive of an effect without a cause, motion could not exist without a force. For Aristotelians, this meant that speed was proportional to force, and inversely proportional to resistance (friction).
• Medieval theories affirmed Aristotle’s external force to be an “impetus.” An object moves in a straight line due to impetus, and once the impetus is consumed, the projectile falls to the ground.
Cannon warfare in the Renaissance showed projectiles moved in a smooth curve, yet they were understand what this curve was.
How Did He Make Them?
unable to
To measure time intervals, Galileo needed a clock of some sort since he had not yet invented the pendulum clock. So he used a simpler, less accurate method: a klepsydra (an ancient water clock), or a large water vessel placed in an elevated position. He attached a small diameter pipe to the bottom of the vessel, whose thin jet of water emptied into a small glass during the time each ball descended. After each ball’s descent, he would weigh the water that had flowed out on a very accurate balance. The water that had flowed out measured the elapsed time, and then he
1 Stamp, Phillip. Optics and the Nature of Light. 2012 Class Notes. Dr. Stamp’s class notes. •8•