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rop a sheet of paper Crumple it, and then drop it again Drop a rock or a pebble How do the three motions compare with each other Do heavier objects fall faster than lighter ones A light, spread-out object, such as a smooth sheet of paper or a feather, does not fall in the same manner as something more compact, such as a pebble Why As an object falls, it bumps into particles in the air For an object such as a feather, these little collisions have a greater effect than they do on pebbles or rocks To understand the behavior of falling objects, first consider the simplest case: an object such as a rock, for which the air does not have an appreciable effect on its motion The term used to describe the motion of such objects is free fall, which is the motion of a body when air resistance is negligible and the action can be considered due to gravity alone

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About 400 years ago, Galileo Galilei recognized that to make progress in the study of the motion of falling objects, the effects of the substance through which the object falls have to be ignored At that time, Galileo had no means of taking position or velocity data for falling objects, so he rolled balls down inclined planes By diluting gravity in this way, he could make careful measurements even with simple instruments Galileo concluded that, neglecting the effect of the air, all objects in free fall had the same acceleration It didn t matter what they were made of, how much they weighed, what height they were dropped from, or whether they were dropped or thrown The acceleration of falling objects, given a special symbol, g, is equal to 980 m/s2 It is now known that there are small variations in g at different places on Earth, and that 980 m/s2 is the average value The acceleration due to gravity is the acceleration of an object in free fall that results from the influence of Earth s gravity Suppose you drop a rock After 1 s, its velocity is 980 m/s downward, and 1 s after that, its velocity is 1960 m/s downward For each second that the rock is falling, its downward velocity increases by 980 m/s Note that g is a positive number When analyzing free fall, whether you treat the acceleration as positive or negative depends upon the coordinate system that you use If your coordinate system defines upward to be the positive direction, then the acceleration due to gravity is equal to g; if you decide that downward is the positive direction, then the acceleration due to gravity is g A strobe photo of a dropped egg is shown in Figure 3-14 The time interval between the images is 006 s The displacement between each pair of images increases, so the speed is increasing If the upward direction is chosen as positive, then the velocity is becoming more and more negative Ball thrown upward Instead of a dropped egg, could this photo also illustrate a ball thrown upward If upward is chosen to be the positive direction, then the ball leaves the hand with a positive velocity of, for example, 200 m/s The acceleration is downward, so a is negative That is, a g 980 m/s2 Because the velocity and acceleration are in opposite directions, the speed of the ball decreases, which is in agreement with the strobe photo.

With all that in place, Build & Run your app. You should now find that you can drag the controls around, with the curve following every move, and the numbers in the text fields changing as you drag.

Figure 3-14 An egg accelerates at 980 m/s2 in free fall If the upward direction is chosen as positive, then both the velocity and the acceleration of this egg in free fall are negative

1 Compare and Contrast How do the currentvoltage curves for a diode, an LED, and a resistor compare 2 Which of these devices follow Ohm s law 3 Analyze and Conclude Diodes are described as having a turn-on voltage What is the turnon voltage for a silicon diode For the LED you used 4 Explain Why would the specifications for an LED give a light output at a specific current, such as 20 mA

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