Balance the Forces within a Mobile
How to Make a Balanced Mobile Step 1. Make sure the strings you tie to your top most rod are the same distance from the middle. Making the strings the Step 2. Weigh all of the shapes on the right side of the rod. Then weigh all of the shapes on the left side of the rod. Step 3. Move on to the. If you have a precision scale, then it's simple:) Weigh what you're putting at each end of the rod (separately). Each rod is simply a lever, and balancing simply means the moments of inertia are equal. That is, m 1 ?L 1 = m 2 ?L 2. Here's a simple numerical example.
The mobile of hanging weights is perfectly balanced. Solve for the values of xyand z. Ignore the weight of the rods and strings. I will use the words weight and mass interchangeably for this puzzle. Or keep reading. MindYourDecisions now has over 1, free articles with no ads thanks to community support!
Help out and get early access to posts with a pledge on Patreon. How to balance a hanging mobile a balanced mobile, the torque on the left and right sides will be equal to each other. In a simple system of two hanging weights, we will have the equation:. We star wars what happened to ahsoka have two equations: one stating the total mass is 30 kg, and another stating the torque on each side is equal.
So we get the equations:. We now have solved the entire left side of the mobile. I run the MindYourDecisions channel on YouTubewhich has over 1 million subscribers and million views. As you might expect, the links for my books go to their listings on Amazon. As an Amazon Associate I earn from qualifying purchases.
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Skip to content. Watch the video for a solution. What Are The Missing Weights? We can then take the system on the left as a single mass m 1. We can concentrate what range can the human ear hear that system.
I studied Economics and Mathematics at Stanford University. Previous Previous post: A Golden Equation.
Nov 25, · In a balanced mobile, the torque on the left and right sides will be equal to each other. In a simple system of two hanging weights, we will have the equation: m1d1 = m2d2 We can begin with the system highlighted in green. Use a second straw and two more shapes to build another balanced structure. Repeat the previous step until you have used up all your cut-out shapes. Now, put all your pieces together to create a multi-layered mobile. Use strings to attach all the straws you made to one another until the mobile is balanced.
Introduction Have you ever seen a mobile? Not a mobile phone—but a hanging art sculpture? You might have had such a mobile in your room when you were little. These mobiles hang in the air and are usually made up of layers of hanging balanced rods, which, in turn, have objects hanging from them. When you look at a mobile sculpture you might wonder how it stays balanced—even when it is in motion.
In this activity you will make your own mobile sculpture and find out. Background Mobiles are free-hanging sculptures that can move in the air. These sculptures are not only artistic, but they are also a great demonstration of balanced forces. If you look at a traditional mobile more closely you will usually notice that it is made of various horizontal rods.
On each of these rods there are hanging objects attached with a string. When building a mobile it is important to keep each rod's objects balanced so that the rod stays horizontal and is not pulled down in any one direction. Each rod essentially acts like a seesaw. If you put more weight on one end of it, gravity will pull the rod down in that direction. To balance the rod you need a counteracting force of the same magnitude on the other side.
It is not only the weight of the objects that matters but also the location on the rod where they are attached. You might notice that not all of the objects are attached to the rods symmetrically, meaning that they are not equally spaced from the pivot point or the center of the rod.
Even with two objects of the same mass the rod can be tilted in one direction if one of the objects is farther from or closer to the rod's pivot point than the other one. A balanced mobile will be at rest as long as no additional forces are acting on its structure. When air moves, however, it can push on the objects hanging from the mobile. As a result they start to move. This motion creates a ripple effect throughout the mobile structure because all of its pieces are connected.
You probably now realize that making a mobile not only requires artistic skills but also some knowledge of physics and balanced forces. You will put all of these skills to the test in this activity by making your own mobile. Do you think you will be able to balance all the forces within its structure? Observations and Results Were you able to balance all the forces within your mobile? It might have been trickier than you thought. Even balancing a straw on a string can be challenging.
You might have observed that if you didn't attach the string to the very center of the straw, it was pulled down on one side more than on the other.
To ensure that the straw hangs perfectly horizontally, the force pulling down on each of its sides must be exactly the same this will be true if the string is in the center of the straw.
When you attached one shape to the straw the weight of the shape should have pulled the straw down on the side it was attached. Attaching another shape to the other side of the straw most likely did not fully balance out the straw either. This was because the shape and size of the two attached pieces were probably not exactly the same.
The shape that was heavier pulled down on the straw more than the lighter shape. You were probably able to balance the straw out by moving the heavier shape closer to the pivot point or center of the straw.
Putting the full mobile together probably took some patience. The mobile probably needed a lot of testing and trying to figure out how to balance the load on each of the straws. You might have noticed that the length of the string didn't affect the balance of the straws very much, as the string itself is not very heavy.
When you hung up the mobile and blew on one of the shapes it should have been obvious that the mobile moves with even the slightest breeze. The air movement pushed on the shape and, even though it was a small amount of force, the whole mobile started moving because all of its parts are connected.
Cleanup Clean up the remaining construction paper, string and all your tools. You can hang the mobile up in your room or give it as a gift. This activity brought to you in partnership with Science Buddies. You have free article s left. Already a subscriber? Sign in. See Subscription Options. Celebrate Math Awareness Month. Shop Now. Materials Heavy construction paper or cardstock various colors work well Hole punch Pen Markers Scissors Tape String Straws, at least 6 Ceiling or doorframe you can hang the mobile from and a chair or adult to help in hanging it Preparation Draw 10 different shapes that you want to attach to your mobile on the construction paper.
The shapes should vary in shape and size. Carefully cut out the different shapes with your scissors. If you like, you can decorate each of them. Punch a hole into the top center of each of the cut-out shapes. Attach a piece of string to each of the shapes by threading it through the punched hole and tying a knot. Try to vary the length of string attached to each shape so that they are not all the same.
Procedure Start with one layer of your mobile. Attach a piece of string to the center of one of your straws. Hold the straw by the string so it is hanging freely in the air. Is the straw hanging horizontally? If not, what do you have to do to make it hang horizontally? Once the straw is balanced tie your first shape to one end of the straw. Again, hold the straw up in the air by its string. What do you notice happens to the straw? Tie a second shape to the other end of the straw then hold the straw up in the air again.
Is the straw balanced? Why or why not? Balance the straw by moving one of the shapes along the straw. Can you find a position on the straw where both shapes are balanced? Use a second straw and two more shapes to build another balanced structure. How easy or difficult is it to balance the two shapes on the straw? Repeat the previous step until you have used up all your cut-out shapes. Now put all your pieces together to create a multilayered mobile.
Use strings to attach all the straws you made to one another until the mobile is balanced. Use different lengths of string so the shapes and straws do not bump into each other. Are you able to balance all the forces within your mobile? Once you have successfully balanced your mobile use tape or string to carefully hang it from the ceiling or a doorframe. When it hangs freely does your mobile move? Carefully blow on one of the shapes hanging from the mobile.
What do you observe? Extra: You have used many strings with a variety of lengths to build your mobile. Find out if the length of the string that you use to attach your shapes to the straw matters. Make them both the same length and then two different lengths. Does it change how the straw is balanced? Extra: Instead of having two different shapes attached to one straw have one shape on one side and another straw on the other side. Then add more shapes or straws to that straw. This is another way to add more layers to your mobile.
How many layers can you build? Extra: Try testing different lengths of straws. What changes if you cut one or more straws in half or use straws with different lengths throughout your mobile? Extra: Can you make a mobile using other materials, such as wooden blocks or other three-dimensional objects? What works best? What are some of the challenges different objects present? Build a Cooler. Make a Potato Shrink--with Saltwater. Get smart. Sign up for our email newsletter.
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