Detroit ins ropes & pulleys

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.
In this investigation we need a load to lift, and naturally the bottom block is it. To really get a good tactile feel of the effect we are looking to investigate, we add some weights to the bottom block, making it much heavier than on its own. This way, we’ll be able FEEL the advantage of using the pulley system to accomplish a task. Use the force scale to measure the weight of the load like the diagram on the slide, and record your result. What does the Force Scale Measure? The force scale measures how much gravity is pulling ( down) on the load ie: its weight. If we apply this exact same force in the opposite direction ( up) while we measure the weight of the load, the load will hang from the end of the scale and not move, the forces are balanced in the up and down direction. If we lift the scale up while we measure the load, we must be applying more force than gravity is applying, and therefore the load is moves in the upward direction. Try this and look at the scale while the load is lifted quickly, it should indicate greater force is applied at this time. The opposite is true when the block is allowed to drop, there must not be enough force being applied to the load, and therefore gravity wins the tug of war and the load moves downward.
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.
Follow Investigation 5.1 Work for this investigation. In this investigation we need a load to lift, and naturally the bottom block is it. To really get a good tactile feel of the effect we are looking to investigate, we add some weights to the bottom block, making it much heavier than on its own. This way, we’ll be able FEEL the advantage of using the pulley system to accomplish a task. Use the force scale to measure the weight of the load like the diagram on the slide, and record your result. What does the Force Scale Measure? The force scale measures how much gravity is pulling ( down) on the load ie: its weight. If we apply this exact same force in the opposite direction ( up) while we measure the weight of the load, the load will hang from the end of the scale and not move, the forces are balanced in the up and down direction. If we lift the scale up while we measure the load, we must be applying more force than gravity is applying, and therefore the load is moves in the upward direction. Try this and look at the scale while the load is lifted quickly, it should indicate greater force is applied at this time. The opposite is true when the block is allowed to drop, there must not be enough force being applied to the load, and therefore gravity wins the tug of war and the load moves downward.
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 & 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

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (19)

Andere mochten auch

Andere mochten auch (11)

Ähnlich wie Detroit ins ropes & pulleys

Ähnlich wie Detroit ins ropes & pulleys (20)

Mehr von Satyam Gupta

Mehr von Satyam Gupta (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

Detroit ins ropes & pulleys

Hinweis der Redaktion