Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.


Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

Column Design (Part 1)

A column in the definition of mechanical engineering does not have to be in vertical. The column is a structural member that carries an axial compressive load, and that tends to fail by elastic instability or buckling rather than by crushing the material. Buckling or elastic instability is the the failure condition in which the shape of the column is not sufficient enough to hold it straight under axial compressive load. At the point of buckling, a radical deflection of the axis of the column occurs suddenly. Then if the load is not reduced, the column will collapse. It's obviously that this kind of failure must be avoided in our machine elements design.

Columns that tends to buckle are ideally straight and relatively long and slender. If a compression member is so short, the normal failure analysis must be used rather than the method that we're going to discuss in this post.

How will we know when a member is long and slender?
The tendency for a column to buckle is dependent on the shape and the dimensions of its cross section and how it is supported.
If we take a look at the cross section of the column, the followings are important properties for buckling.
  1. The cross sectional area, A.
  2. The moment of inertia of the cross section, I, with respect to the axis about which the value of I is minimum.
  3. The least value of the radius of gyration of the cross section, r.
The radius of gyration is computed from

r = sqrt(I/A)

A column tends to buckle about the axis for which the radius of gyration and the moment of inertia are minimum.
From the above picture (thin plate h x t) , we can calculate the value of radius of gyration about x-x axis and y-y axis as shown above. From calculation, we can see that ry-y is less than rx-x because t < h. Therefore, the expected axis of buckling is y-y. We can imagine that we press a common ruler with an axial load of sufficient magnitude to cause buckling, and we can easily imagine how it will bend. The formula of radius of gyration is the tool to predict this phenomenon.

Let's explore more in the next post and make excel sheet to calculate.

Comments

Post a Comment

Popular posts from this blog

Hoekens Straight-line Mechanism

Image
The Hoekens linkage is a four-bar mechanism that converts rotational motion to approximate straight-line motion. The Hoekens linkage is a cognate linkage of the Chebyshev linkage . " DESIGN OF MACHINERY " by Robert L. Norton shows the link ratios that give the smallest possible structural error in either position or velocity over values of Δβ from 20° to 180°. The followings are some interesting examples of Hoekens straight-line mechanism from youtube. Walking robot Marble machine Source: http://www.designofmachinery.com/DOM/Chap_03_3ed_p134.pdf http://en.wikipedia.org/wiki/Hoekens_linkage http://www.youtube.com/watch?v=AkI1nrq9mMQ http://www.youtube.com/watch?v=-CKgP_cueEw http://www.youtube.com/watch?v=PxpRUpmRdCY  
Read more about this Mechanical Design Article »

Dowel Pins and Locating Pins

Image
Dowel pins are the fasteners used to secure two parts together. They are available in both Metric and English sizes, and carry specifications such as diameter, length, and materials. Most dowel pins are made of stainless steel, plastic, , hardened steel, or ground steel. Plastic dowel pins are made of thermoplastic or thermosetting polymers with high molecular weight. Stainless dowel pins are chemical and corrosion resistant, and have relatively high pressure ratings. Dowel pins are often used as precise locating devices in machinery. Stainless dowel pins are machined to tight tolerances, as are the corresponding holes, which are typically reamed. A dowel pin may have a larger diameter so that it must be pressed into its hole or a smaller diameter than its hole so that it freely slips in. When mechanical design engineers design the mechanical components, typically they use dowel holes as reference points to control positioning variations and attain repeatable assembly quality. If
Read more about this Mechanical Design Article »

Ball Detent Torque Limiter: Overload Clutch

Image
A torque limiter is an automatic overload clutch that provides machine protection and reduces repair time during jamming load conditions. This is done to protect expensive machines and prevent physical injuries. A torque limiter may limit the torque by slipping (as in a friction plate slip-clutch), or uncouple the load entirely (as in a shear pin). Ideally the torque limiter should be placed as close as possible to the source of the jam. This will allow the system inertia and torque to be quickly and effectively disconnected from the jammed section. The system can then be allowed to stop without causing further machine damage. A mechanical torque limiter will provide faster response times and better protection than typical electronic methods at high crash rates. There are several disconnect types available, but we will focus at the Ball Detent type . A ball detent type torque limiter transmits force through hardened balls which rest in detents on the shaft and are held in pl
Read more about this Mechanical Design Article »