The goal of this project, when complete, is to have a working scale. It should be able to tell you the mass of any object given that it is between two as of now unknown limits. When it is done, these limits will be known and will be specified to the freshmen when they are in the EG 120 class.
One of the most important things about the experience will be what it teaches to the freshmen. They will learn Newtonian physics, since that is where all of these formulas used to determine the mass come from. This will serve to reinforce the material they are learning in freshman physics and will help them as they move on to their more specific engineering. They will also learn about real-world systems and how any sort of action upon the system can have a major effect. Teamwork will also be a benefit to this experience as the combination of different types of engineers learns how to work with people who do not always understand things in the same way that they do. They will learn to identify problems like this and break it down into minor sub-problems or tasks that can be done by different individuals. They will have to learn to split work up and to not give anyone a free ride on the project. The project will also serve as abstract modelling of the real world as they will see on a smaller scale how an actual piece of equipment that they have used in their life actually works. They will start to understand that things are designed and implemented certain ways so that they can work successfully.
This project also teaches competition, which will show them what the real world is like. Because in this world, being the very best does not always mean being the most accurate or efficient. Sometimes it is better to be first. Performance measures that can be used with the scale are the degree of accuracy it will give and the upper limit for a mass. These both provide possibilities for optimization as our project will show. Also, the experience teaches how to make something work with only limited resources. The freshmen will only be given certain limited materials and be told to make the scale. There will be different styles available for them to use to make it. We have thought of five or six different ways ourselves to make a scale.
One big benefit of this project to all engineers is the use of computers. Computers are the future so anyone who wants to do anything should know how to use them. This project forces some programming to be done in order to accomplish the designated goals. The interface between the Legos and the computer must also be learned to be optimized. Control of various elements within our scale will all be done through the computer. Movement of various details will be forced through the pressing of a button on a keyboard.
One major benefit we saw with our scale was that their is no one clear cut way to implement it. We have a see-saw balance where we will move the pivot in different directions in order to determine the mass. There is the traditional balancing pan scale. There is one where, by measuring the distance a mass moves a hanging spring , we determine the mass. Another uses simple harmonic motion to measure the mass. Placing a mass on the other end of a see-saw scale from a tank of water while knowing the volume of water will determine the unknown mass.
We have different complex solutions to our scale. We teach a lot with this project, but it is also a lot of fun to see how to build this in various forms. We feel this experience would be rewarding for any engineering student, be they freshmen or seniors.
The Variant Pivot Point
In this method of designing a scale, we used the standard balance beam with a pivot point. When the pivot point is centered the beam or rod should balance on its own, but when the pivot point is moved it loses its balance immediately. In order to maintain balance, a force has to be exerted on the opposing end.
Knowing the distances between the pivot point and the ends of the beam one can find the mass of a given object. Or equally, given a non-centered pivot point and given a know mass the object would be to place the weight at a certain distance on the opposing end to balance the beam. This is the model for most scales found in physics lab or in corner stores. For the design, the project will vary the location of the pivot point on the beam and then then try to locate and maintain balance in order to mass an unknown object.
The basis for this design is the concept of torque using the equation M1L1=M2L2. The product of a force and its perpendicular distance to a point of turning, also called the moment of the force. Torque produces torsion and tends to produce rotation.
The legos are to simulate this design and concept in order accurately obtain the mass of a given object by using the equal and opposite forces. One solution is the following design.
By using the formula, one can obtain balance and determine the approximate mass of the object, given an object of known mass.
The Hanging Spring
One of the possible ways to implement a scale, using Legos as well as other things, like a spring and some simple rope, would be our idea of a hanging spring. This spring would hang from a fixed location, high enough that when a mass is attached to its end, it would be allowed to extend without the mass touching the floor. There would be a light upon the end of the spring. This light will serve to enable accurate measurement of the mass.
When the mass was hooked to the end of the spring, the spring would extend. Now, over to one side of the experiment we would have a pulley set up with a mechanized reel. The reel would hold string that would extend up and through the pulley and would have a light sensor tied on to the string. When the mass has extended the spring, the reel would slowly let out more string. This movement would continue until the sensor reaches where the light on the spring has stopped. The distance it moves would be measured and used in the mass calculation.
That calculation would be done using the formula F= kx. The force F is equivalent to the spring constant k multiplied by the distance the spring moved x. Force is also equal to mass times acceleration so these two equation can be combined to determine the mass. The final equation would be:
Therefore, the mass could be calculated. The constant for the spring would be known and acceleration will also be known as it is gravity. Therefore, this would leave the experiment only dependent upon one measurement by the experimenter, which would be the light sensor in this case. Therefore, there would be less possibilities for error.
The Weightless Balance
There are several ways to design a massing device that goes beyond the traditional balance approaches. In fact, two of these designs do not even require the presence of gravity to function. This is a very necessary property for running experiments in space, and it will require the students to think beyond their normal experience. The designs presented below make extensive use of freshman physics and tie directly into some of their physics laboratory experiments.
There are at least two ways one can design a weightless balance (also known as an inertial balance). They both rely on the use of a simple coiled spring. A flat spring can also be used, but it is probably somewhat easier to connect a coil spring to LEGO blocks. The first design measures motion in the horizontal direction. The design looks something like this (obviously not using LEGO):
As shown in the figure, a spring connected to a mass causes
it to oscillate back and forth with a definite period. This period is
determined entirely by the mass of the object. The equation governing
this relationship is
In this equation, k is the spring constant, which must be measured in
advance. This can be done by hanging a known mass from the spring and
observing the distance the string stretches. The spring constant is
then obtained with Hooke's Law:
The period of motion could easily be measured using the LEGO Lamp/Light Sensor pair by placing the lamp and sensor opposite each other with the mass moving between them. A light blocking apparatus on top of the container carrying the mass would interrupt the sensing of the LEGO lamp. Successive interruptions of the light could be timed to obtain the period.
This design suffers from the friction force between the object and the horizontal platform. A simple modification takes us to the second design, which uses vertical motion:
The period of motion is found by applying the same formula as in the horizontal scale:
Again, the Lamp/Light Sensor pair can be used to measure the time between successive interruptions of the light to obtain the period. The main problem with this design is that the equilibrium point of the hanging mass is not known until it is attached to the spring. Since the amplitude of motion can vary, it would be best to position the light sensor at the equilibrium point so that interruptions of the light are guaranteed to occur. Thus, after hanging the mass, the sensor would have to be moved to this point. This should not be too difficult to do, but it is an inconvenience.
These designs require very little that is not included in the LEGO kit. In fact, about the only extra item required is a spring. Some extra flat Legos may be required, especially if the students choose to implement the horizontal inertial balance design.
Engineering Concepts and Project Enhancements
The LEGO scale project will introduce freshman to several aspects of engineering. Because so many designs are possible, the students can be quite creative. Problem solving is a fundamental skill developed in this project, due to the many possible designs. The students must decide on the best strategy for partitioning the problem and assigning responsibilities to group members.
Freshman physics also plays a crucial role in this project. The students will put theoretical equations to practical use, and will more than likely discover that theory does not translate directly into reality. There will be many problems that require work-arounds . Calibration is an issue with any measuring device. With a scale, the mass of the pan holding the object must be taken into account. In the case of a spring scale, the spring constant must be determined. These are things that the design could be made to do automatically.
A great addition to this project would be some sort of robotic arm that loads masses or moves the pivot point to balance a scale. This not only introduces potential mechanical engineers to concepts in robotics, it also introduces feedback into the system, as the robot must continually compensate for the unknown object when trying to balance the scale. Feedback also plays a crucial role in the moving pivot scale, and the computer must decide which in which direction to move the pivot. Feedback and adjustment are fundamental engineering concepts, and they also make the project much more interesting and challenging. A robotic arm also allows computer science hopefuls to play around with real-time programming to control the arm.
Performance Measures
The most obvious measure of the success of a scale design
is whether it can mass objects accurately. Getting an accurate scale
will require a lot of experimentation and adjustment. Students who
put in the extra time will definitely see a payoff. A contest could
consist of massing several objects to see which design comes closest
to the actual mass. Speed could also be a factor in a competition. A
pan balance design loaded by a robotic arm is a perfect example. The
program must decide which known masses to use to try to balance the
scale. A program that simply runs through all possible combinations
until it finds a solution will take much longer than one that picks
more intelligently, such as halving or doubling the current mass
depending on the circumstances.
Conclusion
A scale design should be able to be constructed in the 2-4 week period given for the projects, if the students formulate a plan before they start building things. When discussing this proposal, it only took about 30 minutes for us to come up with 5 or 6 different designs. Implementing these designs using Legos will most likely take a bit longer.
The LEGO scale project introduces many engineering concepts to freshman students. The incorporation of Newtonian physics will bridge the gap between theory and reality. Robotics and feedback can be easily incorporated into the project to make it more interesting. Most importantly, the students will learn about how to combine solutions to small problems in order to design a complete system.
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