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# Detroit ins ropes & pulleys

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• Intergrated Science is a new hands-on program developed in-house by CPO Science Note to presenter: This follows Investigation 4.2 Materials: Students work in groups of three to four at tables. Each group should have: Lever with carriage bolt and black knob 4 Lever strings Physics stand Weight set
• Simple machines transform input forces into output forces. The concept of mechanical advantage is the measure of how much the forces are increased or possibly decreased. When we use simple machines, we apply an input force to accomplish some task, and the machine converts it into an output force that makes the task easier, or provides us with a more convenient option to accomplish the task. For instance, we can climb a ladder, or we can go up stairs( a kind of ramp ) to reach to top of a tower. Either way, we wind up the same height off the ground. However, the stairs allow us an easier option than the ladder to reach to the top.
• Mechanical systems and machines require an input force to achieve an output force. Pulleys can have one supporting strand, like the simple diagram, or more than one, like the pulley system used to lift the elephant. That kind of pulley arrangement is called a block and tackle.
• The Red strings just keep the lower and upper block together when not in use and simply provides the support while hanging. Once the yellow string is pulled on, the red string no longer provides support, and you’ll see it just sag as the weight of the lower block becomes supported by the yellow string. The yellow string supports the block while lifting, and can take different configurations as we experiment with different ways to loop it through the pulley system.
• We have two places we can attach the string, the bottom block or the top block. Both options lead to the string eventually going up and over the top pulley set so we have a string to pull on. But there really is a difference; When connected to the bottom block, there is a total of one string supporting the weight and providing the lifting force, just that one strand of yellow string. When connected to the top, and threaded down and then up and over, there is actually two strands of strings supporting the weight and providing the lifting force. Try these two set ups and see if you can feel a difference in the force required to lift the weight of the bottom block.
• This is Investigation 4.1 and you can follow along with your handout/Investigation Manual. When there is just one supporting string, that one string is supporting all the weight of the load. Lifting the load by pulling the string means that the output force of the string has exceeded the weight force of the load, so it moves up. Lowering the load means that the output force is less than the weight, and it moves downward. The average of these two values applied to the string will be the value we use for the input force. With only one supporting string, we’ll see that input force = output force. The force required to lift the load will be equal to its weight.
• When there is just one supporting string, that one string is supporting all the weight of the load. Lifting the load by pulling the string means that the output force of the string has exceeded the weight force of the load, so it moves up. Lowering the load means that the output force is less than the weight, and it moves downward. The average of these two values applied to the string will be the value we use for the input force. With only one supporting string, we’ll see that input force = output force. The force required to lift the load will be equal to its weight.
• With either set up, the # of supporting strings can be increased. This is done by unclipping the string and threading it up and over or under and up both pulley sets. Doing this can allow for up to 6 strings to be used to support the load. It turns out there can be either odd, or even #s of supporting strings depending on whether the top or bottom block is the attachment site. You can see that unclipping the string on the one supporting string set up, threading it under the bottom pulley set, and then up and clipping it to the top block will create a two string support set up. From here, we can unclip the string, go up and over and clip it to the bottom block and we’d have three supporting strands. By continuing this process we can work our way all the way up to 6 supporting strings. At each set up the input force to hold the block up should be measured, and recorded in the data table provided. Interesting Aside : Some of the more creative people may discover that the string can continue to be looped around and around. We’ve gone up to 12 supporting strings, and it really makes a difference. However, since so many sets of strings are rubbing against one another when they are double-looped, friction begins to add up and offset the additional mechanical advantage gained. This happens when; Total Frict. of strings rubbing+Total Frict. of pulleys=Weight of load/# of sup. strings
• Each new strand of supporting string that is added to the total # of supports provides lift. When there is one string, the force is the weight of the load. When there is two strings, the force is half the weight of the load. When there are three strings, the force is one-third the weight of the load. This pattern continues throughout the Investigation. The total weight is split up evenly between each supporting string, and that is the force required to hold the load in place. Any extra force applied to the string by pulling will result in more lift up than the downward pull of gravity and the load will move up. Anything less than this and the load will move down. Just the right amount, and the load will stay put, because the net force acting on it is zero.
• The Mechanical Advantage is calculated by dividing the Output Force by the Input Force. This is used for ANY simple machine. After the trials for 1-6 strings have been completed it is time to look at the results obtained. It becomes clear that the more strings used to support the load, the force needed to lift the load decreases. We call this an Inverse Relationship. The relationship between the mechanical advantage and the # of strings supporting the load may become much clearer at this point.
• The mechanical advantage of a pulley system is equal to the number of strings. Each string helps to share the load, and thus reduces the amount of force required to lift it. However, we find we have to pull much more string through the pulley as we add supporting strings. We don’t get something for nothing; Less force required means more string needs to be pulled. It may take longer, and it may take lots of string, but with pulleys, really heavy loads can be lifted without a lot of force.
• We found out that there were a couple of ways to calculate the mechanical advantage of a lever. Output Force/Input Force and also Input arm length/Output arm length. Both of these relationships would give us the same ratio. From these relationships we can see that both force and distance are conserved in simple machines. This principle enables us to generate large forces from small forces, which comes in very handy all the time. Now we’ll investigate how this applies to the ropes and pulleys.
• We define work to be Force x Distance. Work is done when mass experiences acceleration ( Force ) over a given distance. The unit we use to measure work is the joule. The joule = 1 newton x 1 meter. For work to be done, two things need to happen 1. Force is applied, and 2. Something is moved a distance by the force.
• These two distances that we will be measuring are key to accurately figuring out the work involved. Using the cord stops on the length of yellow string is an easy way to measure the distance of srting being pulled. Start with both stops at the top, pull the string the length desired, and then slide the one closer to the pulleys back up to the top where they were at the beginning. The distance between the two will be the Length ( L ) needed for the investigation. This is the distance that the string has been pulled. The Height ( H ) is easier to measure. By noting a spot on the lower pulley that is at the same height as one of the holes on the stand pole, simply raise the block up successive increments of one hole higher. The holes are 5 cm apart which makes distance measurements easy. The students can raise the block up the same Height for each trial, so only the Length of string pulled will vary.
• When there is just one supporting string, that one string is supporting all the weight of the load. Lifting the load by pulling the string means that the output force of the string has exceeded the weight force of the load, so it moves up. Lowering the load means that the output force is less than the weight, and it moves downward. The average of these two values applied to the string will be the value we use for the input force. With only one supporting string, we’ll see that input force = output force. The force required to lift the load will be equal to its weight.
• Each new strand of supporting string that is added to the total # of supports provides lift. When there is one string, the force is the weight of the load. When there is two strings, the force is half the weight of the load. When there are three strings, the force is one-third the weight of the load. This pattern continues throughout the Investigation. The total weight is split up evenly between each supporting string, and that is the force required to hold the load in place. Any extra force applied to the string by pulling will result in more lift up than the downward pull of gravity and the load will move up. Anything less than this and the load will move down. Just the right amount, and the load will stay put, because the net force acting on it is zero.
• This calculation is done after all the data has been collected. We will perform this calculation for each of the 6 trials.
• The Work Relationship is practically equal for this Investigation.
• We see after doing the calculation for Work that the two are very close. You have to pull more string as the force required goes down. Mechanical Advantage can help us increase our Input Force, but it comes at a price; We’ll also need to increase the amount of string to be pulled. This simple rule applies to all simple machines. In the lever, the forces were weights like what we just used here, and the distances involved were the lengths of the Input &amp; Output arms. Similar variations apply to all the other forms of simple machines
• As the Inv. progresses, it becomes obvious that the amount of string needed to continue to lift the block the same height mounts up quickly. The Force required decreases by half with the first arrangement, so that too becomes clear. After the calculation of the Work IN and Work Out, it makes sense that these should have close to the same value. (Any discrepancies you may have seen were probably due to limitations in the force scale used in the Inv.) Why would the Output less than Input? Our old nemesis Friction. Friction “ takes “ some of the Input Force, which reduces the total Output Force, and consequently the Work Output. The better a simple machine reduces friction, the closer the Work Input and the Work Output will match.
• The rate at which work is done in units of time is called Power. Much in the same way there is a relationship between Speed, Distance and Time, there is a relationship with Power, Work and Time.
• The work-energy theorem defines energy as the ability to do work. We can store energy in objects in many different ways. Batteries are an example of stored energy, as is a tightly coiled spring or a boulder high on a mountain. Each have the ability to do work.
• This is where the concept of energy enters the vocabulary, and since we have just learned about work, the transition makes a lot of sense when we think of energy as stored work and/or the ability to do work.
• ### Detroit ins ropes & pulleys

1. 1. Integrated Natural Science
2. 2. Integrated Natural Science for Detroit Public Schools Ropes and Pulleys Kat Woodring
3. 3. Key Questions: <ul><li>4.1.1 Explain the function of simple machines. </li></ul><ul><li>4.1.2 Differentiate input and output forces and diagrams all forces. </li></ul><ul><li>4.1.3 Calculate the mechanical advantage of a simple machine. </li></ul><ul><li>4.1.4 Relate the concepts of simple machines to the human body. </li></ul><ul><li>4.1.5 Calculate advantage mechanical using input and output. </li></ul>
4. 4. Michigan Content Expectations <ul><li>P3.2B Compare work done in different situations. </li></ul><ul><li>P3.2C Calculate the net force acting on an object. </li></ul><ul><li>Qualitatively and quantitatively explain forces and charges in motion. </li></ul>District Outcomes
5. 5. Simple Machines Include: <ul><li>rope and pulley </li></ul><ul><li>wheel and axle systems </li></ul><ul><li>gears </li></ul><ul><li>ramps </li></ul><ul><li>levers </li></ul><ul><li>screws </li></ul>
6. 6. Pulleys as Simple Machines <ul><li>Simple machines can change the direction and/or magnitude of an input force </li></ul>
7. 7. Pulley Investigation #1 <ul><li>Add 3 weights the bottom block </li></ul><ul><li>The bottom block and the weights are the load to be lifted. </li></ul><ul><li>Use the force scale to measure the total weight of the load. Record it. </li></ul>
8. 8. Pulley Investigation #1 <ul><ul><li>Why does the pulley have so many strings? </li></ul></ul><ul><ul><ul><li>The yellow string is the one we pull to lift the lower block, it then supports the block and transfers the lifting force to the block. </li></ul></ul></ul><ul><ul><ul><li>Red safety strings support bottom pulley block only when hanging </li></ul></ul></ul>
9. 9. How Can We Lift the Block? <ul><li>1. We can attach the yellow string to the BOTTOM block and then thread it up and over the top set of pulleys and pull </li></ul><ul><li>OR…. </li></ul>2. We can attach the yellow string to the TOP block, thread it down through the bottom pulley set and then up and over the top set of pulleys and pull.
10. 10. Measure the Input Force <ul><li>Attach the Spring Scale to the pulling end of the yellow string. </li></ul><ul><li>Pull on the string and lift the load - read the value from the scale as this happens. </li></ul><ul><li>Lower the load with the string - again read the scale as this happens. </li></ul><ul><li>Average the two values from the scale - this is the value of your Input Force. </li></ul>
11. 11. Measure the Input Force for Two Supporting Strands <ul><li>Unclip the yellow string from the bottom block. </li></ul><ul><li>Thread the string through the lower set of pulleys. </li></ul><ul><li>Attach the yellow string to the top block. </li></ul><ul><li>Repeat the input force measurement process for TWO supporting strings. </li></ul>
12. 12. Looping the String Around the Pulleys Supporting strings #: 1, 3, 5 Supporting strings #: 2, 4, 6
13. 13. Forces Involved <ul><li>The weight of the load does not change, it is the same for each trial. </li></ul><ul><li>The output force will be the force required to hold the load still– it does not change since the weight remains the same </li></ul><ul><li>As more strings are added, the input force required to achieve the same output force decreases. </li></ul>
14. 14. Mechanical Advantage <ul><li>Ratio of Output Force to Input Force </li></ul><ul><li>Follows simple pattern with Ropes and Pulley system </li></ul>
15. 15. What is the Mathematical Rule? <ul><li>We found that the input force required to lift the load decreased as the # of supporting strings increased. </li></ul><ul><li>What is the relationship? </li></ul><ul><li># of strings x Input Force = Weight of load </li></ul><ul><li># of strings = Mechanical Advantage </li></ul>
16. 16. Key Questions: <ul><li>4.1.1 Explain the function of simple machines. </li></ul><ul><li>4.1.2 Differentiate input and output forces and diagrams all forces. </li></ul><ul><li>4.1.3 Calculate the mechanical advantage of a simple machine. </li></ul><ul><li>4.1.4 Relate the concepts of simple machines to the human body. </li></ul><ul><li>4.1.5 Calculate advantage mechanical using input and output. </li></ul>
17. 17. Mechanical Advantage For the Lever <ul><ul><li>Two ways to calculate mechanical advantage: </li></ul></ul><ul><li>Output Force/Input Force </li></ul><ul><li>Input arm length/Output arm length </li></ul><ul><ul><li>We can use this to generate large forces from much smaller forces. </li></ul></ul>
18. 18. Work <ul><ul><li>We define and measure work in a very specific way in science. </li></ul></ul><ul><li>Work = Force x Distance </li></ul><ul><li>One joule of work is accomplished when 1 newton of force is used to move an object a distance of 1 meter </li></ul>
19. 19. Pulley Investigation - #2 Work <ul><li>Transfer the data you recorded as your Output Force from investigation 4.1 to the Data Table in 4.2. </li></ul>
20. 20. Pulley Investigation - Work <ul><ul><li>What distances are we measuring? </li></ul></ul><ul><ul><ul><li>Input :The length of the yellow string that is pulled to lift the block ( L ). </li></ul></ul></ul><ul><ul><ul><li>Output : The height of the block after it is lifted; the distance it is lifted ( h ). </li></ul></ul></ul>
21. 21. Measure the Input Force <ul><li>Attach the spring scale to the pulling end of the yellow string. </li></ul><ul><li>Pull on the string and lift the load - read the value from the scale as this happens. </li></ul><ul><li>Lower the load with the string - again read the scale as this happens </li></ul><ul><li>Average the two values from the scale - this is the value of your input force . </li></ul>
22. 22. Forces Involved <ul><li>The weight of the load does not change, it is the same for each trial. </li></ul><ul><li>The output force will be the force required to hold the load still– it does not change since the weight remains the same </li></ul><ul><li>As more strings are added, the input force required to achieve the same output force decreases. </li></ul>
23. 23. Data Collection <ul><li>We will be taking the data at all 6 of the pulley arrangements. </li></ul><ul><li>Compare the data at each arrangement: </li></ul><ul><ul><li>What changes and how? </li></ul></ul><ul><ul><li>What stays the same? </li></ul></ul><ul><li>Do the calculations for the last two columns ( Work Output & Work Input ) after all the data has been collected . </li></ul>
24. 24. Work Calculation <ul><li>The joule is the unit used to measure work in this Investigation. </li></ul><ul><li>Work Input = string length x input force </li></ul><ul><li>Work Output = height change x output force </li></ul>
25. 25. Work Relationship <ul><li>As the # of pulleys used increased, the input force required decreased. </li></ul><ul><li>As the # of pulleys used increased, the input length of string increased. </li></ul><ul><li>Work Output was very close (but not equal to) Work Input. </li></ul>
26. 26. Work : You Don’t Get Something For Nothing <ul><li>Work = Force x Distance </li></ul><ul><li>As the Input Force goes down, the Length of string increases. </li></ul><ul><li>It’s a trade off – Force vs. Distance </li></ul><ul><li>You can use less force to lift the same weight as the Mechanical Advantage increases, but you have to pull more string to do it. </li></ul>
27. 27. Input vs. Output <ul><li>The change in force and distance for pulleys is easy to feel while doing the investigation. </li></ul><ul><li>In fact, Work Output is always less than Work Input. </li></ul><ul><li>Where does it go? </li></ul><ul><li>Friction </li></ul>
28. 28. Power - the rate at which work is done <ul><li>Rates are often measured in terms of time </li></ul><ul><li>Speed = Distance / Time </li></ul><ul><li>Work = Power x Time </li></ul><ul><li>Power = Work / Time </li></ul>
29. 29. The Work – Energy Theorem <ul><li>The total amount of work that can be done is equal to the total amount of energy available. </li></ul><ul><li>Objects cannot do work without energy . </li></ul><ul><li>Energy is the ability to do work. </li></ul><ul><li>Energy is also measured in joules - it is stored work. </li></ul><ul><li>Energy can be stored for later use. </li></ul>
30. 30. The Work – Energy Theorem <ul><li>Energy can be converted or transformed from one form to another. </li></ul><ul><li>Anything with energy can produce a force that is capable of action over a distance. </li></ul>