Galileo's Hypothesis_4

Galileo’s Hypothesis: Pre-Lab https://wcmu.pbslearningmedia.org/resource/nvmm-math-fallingbodies/galileos-falling-bodies/ Watch the video discussion of Galileo’s study of the nature of falling motion and answer the following questions. Use examples from the video to support your answer when appropriate. What’s Your Idea? A 15 lb bowling ball is 150 times heavier than a 0.1 lb bouncy ball. According to Aristotle, how much faster will a bowling ball fall to the ground when compared to the bouncy ball? When you watch the bowling ball and the bouncy ball fall to the ground, which hits the ground first? At the beginning of the video, you see the video host Adam Steltzner drop a feather and a hammer at the same time. Later on, you see the same demonstration performed on the Moon by Apollo astronaut David Scott. Describe what you see in each demonstration and explain why they have different results. How did Galileo study the motion of a falling body? Describe Galileo’s findings about the relationship between distance and time for a falling object. When Adam Steltzner recreated Galileo’s experiment, he used an arbitrary unit of time he called the “Galileo”. If the ramp he constructed had been longer, how many units of distance do you think the ball would have traveled after 4 Galileos? After 5 Galileos? After 6 Galileos? Explain how you can solve this problem using Galileo’s reasoning about the relationship be distance and time for an accelerating object. Galileo’s Hypothesis: All objects experience the same acceleration downward when falling without air resistance. Measuring the acceleration of free-fall, g, is not a simple thing to do. Galileo had a great deal of trouble in his attempts to measure g because he lacked good timing devices and the motion changed much too quickly. To study accelerated motion, Galileo use inclined planes to effectively reduce the effect of gravity, thus slowing the motion considerably for detailed study. Among other things, Galileo discovered that the distance traveled by an accelerating body is proportional to the time interval squared: distance ∝ time 2 . We now know the complete relationship; for an object starting from rest, distance = 1 2 ∙∙ ( acceleration ) ∙ ( time ) 2 The earth has air which affects the feather more as the feather is resistant to air on the moon where this affect isn’t prevalent due to the absence of air the feather isn’t affected 15 times as fast Galileo used a ramp and measure the distance the rolling ball would travel down the ramp 4 Galileos =15 5 Galileos =22 6 Galileos =30

d = 1 2 ∙∙a∙t 2 A ball dropped from rest will travel a distance ( d ) in a time ( t ) predicted by this same relationship since “falling” is merely a case of uniformly accelerated motion (in the absence of the effects of air resistance). Through careful measurements of the distance and time of fall, the acceleration of the falling body can be determined. Rearranging the distance formula, we get a = 2 d t 2 which allows an easy computation for the acceleration of a falling body. Experiment: When an object falls without air resistance, we say that it is in free-fall and that its acceleration constant. Working in your group, determine how to best measure the time of fall for a stone released from a height of 2.00-m above the floor and calculate the acceleration of the stone. Time of Fall Measurement: Hand-Drop Method d = 2.00 m % Difference in Drop Times [ high value − lowvalue average of values ] x100 % Average Acceleration (m/s 2 ) a = 2 d t 2 Trial Drop Time (s) 1 1.05 1.05-.60 0.85 52.9% PERCENT DIFFERENCE 2*2 .85 2 5.54m/s 2 2 0.91 3 0.60 4 0.63 5 1.05 Average Drop Time = 0.85S How reliable is you’re measured acceleration value? Defend you’re response citing evidence (data). As you have probably found, measuring the acceleration of a falling body accurately is not the easiest thing to do. The measurement can be improved significantly when the timing is carefully coordinated with the release and impact of the falling body. For the second part of the lab you will use a Free-Fall Apparatus interfaced with a computer to measure the drop time of a steel ball. The computer accurately times the fall from the release of the ball until it strikes a receptor pad directly below. Careful measurements of the distance fallen can then be used in conjunction with the time of fall to compute the acceleration due to gravity (as you have already demonstrated). Measured Drop Distance (Steel Ball) % Difference in Drop Times [ high value − lowvalue average of values ] x100% Steel Ball Acceleration (m/s 2 ) a = 2 d t 2 Trial Drop Time (s) 1 .5673 Very unreliable there is a very high percent difference d = 1.567m m

9.66-9.61 9.63 0.52% 2 9.61 3 9.66 4 9.62 5 9.63 Average Acceleration = 9.63 Is your acceleration measurement reliable? Why do you think so? Yes the percent difference is less than 2%

Analysis Galileo’s law of falling bodies predicts that all objects in free fall accelerate equally, regardless of weight. Looking at all your measurements for the acceleration of a falling body with a critical eye (i.e., taking into account errors involved with any physical measurement), did you find this to be true? To answer this question, you must decide whether or not the measured accelerations for the objects you dropped are statically different. One way to do this is to compute a percentage of difference. If the values are within 5% of each other, they are not considered significantly different and consequently are equivalent within experimental error. Compute the %-difference in your measured accelerations. Measured Accelerations (m/s 2 ) Steel Ball Aluminum Ball Picket Fence 9.81 m/s 2 9.86 m/s 2 9.63 m/s 2 % Difference in Measured Accelerations [ high value − lowvalue average of values ] x100% 9.86-9.63 9.77 2.35% Percent difference Does your data support Galileo’s Hypothesis? Why do you think so? Yes there is a very low percent difference for the different values lower than 5% which was the agreed upon difference