The Educator's PLN

The personal learning network for educators

# Applied Mathematics

The subject of mathematics is related to almost all the other subjects. The advancement in the fields of engineering, science, economics statistics etc. are facilitated by use of mathematics. In other words, the application of mathematics helps in development and easier understanding of topics in other subjects. The branch of mathematics that is used for such a purpose is called as applied mathematics. It may be noted that in this branch of math, the important terms and constants used in the other topics also form as parts.

Let us give a simple introduction to applied mathematics with interesting examples from other fields.

A car leaves an airport at 8 am and runs at an average velocity 45 mph. At 9 am another car leaves the same airport in the same direction and it has to meet the first car before noon. What should be the minimum average velocity with which the second car should run to achieve the necessity?

The situation described in the above physics problem is not very unusual. A person traveling in the first car might have left out something and his friend at the airport may like to reach that article. And by noon, the first person might reach his destination and may not be reachable thereafter. Let us see how applied mathematics helps us to solve. The velocity refers to the rate of change of distance with respect to time. Hence the distance traveled by the first car in the 4 hours (from 8 am to noon) is given by the mathematical equation d1 = v1* t1 = 45*4 = 180 miles, since we know that v1 = 45 mph and t1 = 4 hours. The concept of applied math is same for the second car but now the equation is d2 = v2* t2. But in this case the known values are d2 = 180 miles, since at the point of interception both cars must have traveled the same distance and out of necessity the maximum value of t2 can only be 3 hours (from 9 am to noon). Therefore, 180 = v2*3, which gives the solution as v2 = 60 mph.

Let us study another problem related to physics but which can be considered as an applied mathematics. Two wires of ½ in. diameter are anchored at a ceiling roof as shown in the diagram. These wires are riveted to a hook which is used to hold heavy weights. The wires make angles of 45o and 60o with the ceiling. The wires have an ultimate tensile strength of 16T per sq.in. What could be the maximum weight that can be loaded on the hook?

The concept of this problem is used in material lifting equipment. Ultimate tensile strength of 16T/ sq.in. means the wire can take a load of only 16T for a cross section area of 1 in. Since the diameter of the wires are ½ in. each wire can take only a load of 16(π/4)(1/2)2 = π tons ≈ 3.14 tons. Now mathematically we can draw a vector diagram and find the solution. The same is drawn below.

The wires on the left and right take the loads that are the projection of the main load W in the direction of wires. Let those components be P and Q respectively. As per vector algebra, P = (√2)W/2 and Q =  (√3)W/2. Obviously the magnitude of Q is greater and therefore it must be equal to 3.14T. Hence W can be equal to a maximum of 3.14/0.866 = 3.63T approximately.

The concept of matrices is widely used in statistical fields. We will give an introduction to matrices in our next topic.

Views: 166

Comment

Join The Educator's PLN

Comment by John Marsh on February 3, 2014 at 3:00am

Yes you are absolutely right Marin, you can use same concept for stress and strain calculation.

Comment by Oscar Marin on February 2, 2014 at 4:42am

I never analyzed this concept of applied mathematics, It seems really great. Can that be applied to trigonometric problem solving too. I think this has much of application on work and energy concept of physics where a stress and strain calculation for a particular object or a bridge needs to be calculated. Hope I am right!!

Thomas Whitby created this Ning Network.

## Latest Activity

Christine Hinkley posted an event

### OLC Collaborate - Kansas City at UMKC

September 25, 2018 all day
OLC is heading to Kansas City to meet with online learning professionals, educators, and administrators to address the opportunities and challenges we all face regarding digital accessibility and higher education today.See More
11 hours ago
Sonya Jane Olopai, Henry Trunk, Khalid J Tellis and 1 more joined The Educator's PLN
Friday
Darca Saxton, Yvonne Mercredi, Kyle Renchen and 13 more joined The Educator's PLN
Jun 13
Oliver Maurice posted a blog post

### How to get a PhD

A Ph.D. is the terminal degree for some fields, and it prepares graduates for faculty and research positions at universities. Earning a Ph.D. requires advanced coursework, examinations and a dissertation analyzing original research. This article discusses what must be done to obtain a Ph.D.The first step in the journey toward completing a doctoral degree is to obtain an undergraduate degree. For the best start, choose a bachelor’s degree program at a regionally accredited university.…See More
Jun 13
Jun 10
Jun 10
Oliver Maurice posted a blog post

### Overcoming writers block

Writer’s block is a term you’ve probably heard often. The amazing and confusing thing about writer’s block is that people apply the term to drastically different experiences. For many, “writer’s block” means a frustrating but temporary stall in their progress. For some authors, though, the phrase looms nightmarishly large and describes a recurring and debilitating struggle to move ideas from their mind to the page.Under the pressure of deadlines, almost everyone—from students to professors to…See More
Jun 8
Candace Knihniski is now a member of The Educator's PLN
Jun 7