01_Worksheet_Motion_Mendoza

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107

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Physics

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Apr 3, 2024

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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,

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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.

That would mean that the number could be anywhere from 5.5 seconds to 5.7 seconds, recorded this way: ࠵? = 5.6 ± 0.1࠵? So now let us back off a bit. Could you be off by as much as 0.2 seconds? You think again. You are more confident in this estimation. That would mean that the number could be anywhere from 5.4 seconds to 5.8 seconds, recorded this way: ࠵? = 5.6 ± 0.2࠵? You feel okay telling others that you are at least 70% sure the true value of the time of flight was somewhere between 5.4 seconds and 5.8 seconds. Although this is the last you will hear or read about estimating uncertainty in Physics 107, it is very important because it gives others a sense of how accurate your measurements are, and how much confidence they can put into your overall data, including the calculations based on that data. Back to our data from today: What variable did you change? ______added extra washers_______ Fill in the following table with your numbers. Change Time of Flight (s) Distance from Target (m) Beta (s/m) 1 washer 4.9 0.345 14.2028986 s/m 2 Washers 4.1 1 m 4.1 s/m 3 washers 3.7 1.20 m 3.0 Show complete sample Beta ( ࠵? ) calculation here: Which of your parachutes gave you the best performance? Why do you think that was? The parachute with the best performance is the parachute with 1 washer since it landed closest to the designated point. Add Group Table

When first dropped, we measure the parachute’s position above the floor. At the moment we drop the parachute it has zero velocity . The only significant force acting on the parachute when it first starts falling is the downward force due to gravity. As it falls the velocity increases so the parachute has a non-zero acceleration . Also as it falls the upward air resistance force increases as the velocity increases but is not yet equal to the force due to gravity. At some point the upward air resistance force becomes equal to the downward force due to gravity. At this point the forces balance and the parachute has zero acceleration and falls to the ground with a constant velocity . List the variables you used to describe the motion. Position, velocity, force, acceleration, If we were on campus you would have built a parachute as described in the lab book. You would then drop the parachute from a balcony and measures time of flight and the distance from your target and the landing position. ࠵? = ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?ℎ࠵? (࠵?) ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵? (࠵?) + 1࠵? You want ࠵? to be as large as possible so you want ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?ℎ࠵? to be as large as possible and ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵? to be as small as possible. You would then change one of the variables twice. For example your prototype had one washer. You could then make the same measurements with two washers and then with three washers. Or you could change the length of the strings, the area of the canopy (keeping the same 2 to 1 ratio for the length and width) or number of holes in the canopy. Why do we only change one variable at as time? If we changed two variables at one time we could collect the data faster (but would it be quality data?).

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Eureka Videos We start the Eureka videos on the third video, Speed. We will watch the first two videos later. In this video inertia is mentioned because it was covered in the first two videos. Inertia is related to mass and it is a property of the body. It is a measurement of the body’s ability to oppose attempts to change its motion. If an object is at rest it wants to remain at rest. If a body is in motion with a constant velocity (constant speed in a straight line) it wants to remain in that state. You already understand this concept. If a bowling ball and a basketball are at rest which one would be easier to put in motion? If a bowling ball and a basketball were rolling towards you with the same constant velocity which one would be easier to stop? Speed https://www.youtube.com/watch?v=LMsyYyrS3Bc&list=PL4EE139D689C7CD27&index=3 Acceleration I https://www.youtube.com/watch?v=XTNQaObeC8c Acceleration II

https://www.youtube.com/watch?v=_ChAICt5PRM Variable ( Symbol ) Definition Tools/ formulae Units Position ( x ) Where something is located Ruler, meterstick m, cm, ft, km, miles Velocity ( v ) How fast something is going Meterstick, stopwatch m/s, MPH, km/hr Acceleration ( a ) How fast you are getting fast or how fast you are getting slow. Meterstick, stopwatch m/s 2 1) What is the difference between speed and velocity? Speed is magnitude (just the number) while velocity is magnitude and direction (takes into account all factors such as direction. 2) If a bowling ball and a basketball were both rolling at you with the same constant velocity, and you only had to stop one of them, which one would you try to stop? The ball I would try to stop is the basketball because of the lighter weight. 3) In terms of physics explain why you made this choice. I would choose the basketball because of the inertia of the balls. Both will want to continue rolling down like what Newton described.

n 4) Inches/century would be a unit for what? Velocity because inches describe distance and century describes a time. 5) 32.2 ft/s 2 would represent which of the variables in the above table? Acceleration is what is made with these variables 6) What did Galileo find out about falling objects that contradicted the Greek belief? Galileo found out that falling objects all fall at the same rate since they fell in relation to earth and not their mass. https://www.youtube.com/watch?v=KDp1tiUsZw8 A farmer in an old pick-up truck, and a spoiled rich kid in a new Porsche his parents gave him for his 18 th birthday, leave Sacramento at the same time heading for Redding up I-5. The farmer never stops and travels the whole distance at 45 MPH. The rich kid drives at a constant 90 MPH but stops for a while at a rest area. The rich kid resumes the speed of 90 MPH when getting back on the freeway. The farmer and the rich kid get to Redding at the same time.

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1) What was the farmers average speed? 45 mph 2) What was the rich kid’s average speed? 45 mph 3) How many times and for about how long was the rich kid traveling at 45 MPH? (How many times was the rich kid’s instantaneous speed 45 MPH?) 2 times, to slow down as well as to speed up after leaving the rest area 4) Upon reaching Redding the rich kid is pulled over by the CHP for speeding. The rich kid argues that he should not get a ticket because he stopped at a rest area and therefore his average speed was only 45 MPH. Would the CHP officer, or a judge, buy this argument? Why or why not? No, because his speed once pulling over was much higher than his average of 45 mph, the average takes into account lower speeds which

were in the past and not when he was pulled over.

01_Worksheet_Motion_Mendoza

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