01_Worksheet_Motion_Mendoza

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California State University, Sacramento *

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107

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Physics

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Apr 3, 2024

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pdf

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Physics 107 Worksheet #1 This investigation is about using basic science to think about the design and performance of an object or collection of objects (what we will learn to call a “system”) in the designed world. In this case the system is a toy parachute. The first part of this investigative process we sometimes refer to as “messing around with” or “exploring” the system to see how it performs and to build insight into what influences its behavior. Design projects often start with a prototype—a sample design that has already been built—and then try to improve it. Using words that we commonly associate with scientific investigations, that prototype is the “control” that you will compare the performance of all your new designs to. 1. Use the specifications below to build your original prototype parachute. While you’re building the prototype, think about and discuss in your group what you could change about the components of the parachute to make it “better.” a. Specifications/procedure for building the prototype parachute white plastic sheet two 100 cm pieces of string one washer b. Cut a 50 cm × 25 cm rectangle from your white plastic trash bag. c. Cut two 100 cm lengths of string. d. Tie one side of each string to neighboring corners of the rectangle. e. Place both strings through the washer. • Tie the free ends of each string to the diagonal corner of the rectangle, so that the strings cross to form an " X ". • Try it out by dropping it from the outdoor walkway on the second floor of Sequoia (Building we are in). 25 cm 50 cm 100 cm

Your group will want to take a stopwatch and a meterstick. You want to measure time of flight for the parachute as well as well as the distance it landed from a predetermined target.

When you are down there be careful of the plants and don’t let a parachute hit some innocent bystander on the head. Next you want to change one variable of the parachute twice and also measure time of flight and distance to target. You only change ONE of the variables, and you change that variable twice. For example, your prototype had 100 cm long strings. You can change the strings to 75 cm (But change nothing else) and then to 50 cm (and again change nothing else). The equation we will use to determine the quality of the parachute is the following: We want Beta to be as large as possible. That means we want the time of flight to also be as large as possible but the distance to the target to be as small as possible. You have to consider the trade-off. For example, going from one washer to more washers might lessen you distance to target, but it might also reduce your time of flight. Example of table if color of canopy is changed. Change Time of Flight (s) Distance from Target (m) Beta (s/m) White 5.6 3.12 1.36 Red 6.1 4.26 1.16 Blue 4.8 1.86 1.68 Example of complete sample Beta ( ࠵? ) calculation: ࠵? = ! "#$.&&’ = (.)* +.$,’#$.&&’ = (.)* -.$,’ = 1.3592233 ࠵? ࠵? ⁄ = 1.36 ࠵? ࠵? ⁄ Unlike units, significant digits are something that is not really stressed in this class, but you can see how the first answer above, before rounding, is ridiculous because it claims an accuracy in your data that you do not have! In reality,

because we only had two digits of accuracy in our time of flight, we should have rounded our answer down to 1.4 s/m. Suppose our data looked like this because we had really sophisticated, state-of- the-art, extremely expensive equipment to make our measurements and not just a manually worked stopwatch and a meter stick: Change Time of Flight (s) Distance from Target (m) White 5.6838276 3.1201203 Then: ࠵? = (.).+.,/)* -.$,&$,&+’ = ࠵?. ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵? ⁄ OR Change Time of Flight (s) Distance from Target (m) White 5.6000210 3.1299989 Then: ࠵? = (.)&&&,$&* -.$,000.0’ = ࠵?. ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵? ࠵? ⁄ So, as you can see, we are already off by the third number, and after that they are not even close. Another factor to consider is how accurate are your original measurements. Let us take the time of flight for example. You are the person with the stopwatch. You start the stopwatch just as your lab partner drops the parachute from the balcony. You stop the stopwatch just as the parachute hits the ground. On the stopwatch you read off the number 5.6 seconds. I come along and ask you how accurate do you think that 5.6 seconds time actually is. Could you be off by as much as a second? That would mean that the number could be anywhere from 4.6 seconds to 6.6 seconds, recorded this way: ࠵? = 5.6 ± 1.0࠵? You say there is no way you are off by as much as a second. Could you be off by as much as 0.1 seconds? Now you have to think. You are not confident that your measurement was that accurate.

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