Posts Tagged ‘simple’

h1

Australian Open 2020: Could YOU ….. return Roger Federer’s serve?

January 27, 2020

The Australian Tennis Open is being played at the moment and Mathspig is always amazed at the serve speed of the top-seeded players.

Here are some of the serves speeds of players in this year’s Men’s Open. 

Keep in mind the fastest female tennis serve by Barbora Záhlavová-Strýcová is a very respectable 225 km/h (140 mph).

Can you return Roger Federer’s serve?

NOTE: Andy Murray had the same serve speed as Roger Federer.

Go here to see why this simplified calculation works! 

Mathspig tested her reaction time here. TRY IT!

Mathspig’s best, best, best reaction time = O.33 sec

Could Mathspig return Roger Federer’s serve?

Nooooo!…………………………………………………………………….

I’d be hit in the head by a speeding tennis ball

before I even moved.

But I’m a pig. I’ve got the best service GRUNT! Ha!

h1

Make a Cool Pattern with x2 Tables… but it is trickier than you think.

September 6, 2019

A COOL MIDDLE SCHOOL MATH EXERCISE

This idea comes from Burkard and Giuseppe @ the fabulous MATHOLOGER channel. Students can make a pattern called a cardioid that pops up all over math according to Burkard.

Follow these steps. There is a pdf file below the first diagram for printing exercise sheets.

And then watch the MATHOLOGER video for a really interesting explanation.

x2 Tables on a Circle pdf file for printing

This circle graph blank could also be used for x3 and x4 tables, which produce totally different yet equally amazing patterns.

Halfway there, now it gets tricky. +52 to each point on the circle and keep multiplying by 2.

ie. 27 x 2 = 54, 28 x 2 = 56 and so on.

so 0 = 52, 1 = 53, 2 = 54, 3 = 55, 4 = 56 etc

This shape is called a CARTIOID.

h1

Can you escape a FALLING TREE?

August 24, 2019

Tragically, 5 people have been killed by falling trees in Victoria, Australia, this Winter. 

In 3 separate accidents, 4 died when trees crushed the occupants in cars. One victim was a pedestrian.

So if you were walking through a park could you escape a falling tree if you either heard a cracking sound or saw the tree starting to fall?

With thanks to Physics Stack Exchange.

For an inverted pendulum near the top of its arc, there is no period, but the quantity ℎ/𝑔 does represent a characteristic time scale for this system. The tree will take a few of these characteristic times to fall.

Mathspig hates seeing an old tree felled, but it does give us the necessary time data.

 

There are many assumptions in these calculations.

*You’d be hit by the tree trunk, not a branch which would hit you sooner.

*There is no wind pushing the tree over.

*The tree falling is an approx to a reverse pendulum.

 

h1

Sound Math 1: Good Vibrations!

May 1, 2019

There is so much maths around sound, but sound is simple.

Sound is made by something vibrating in air. The vibrations create waves and these pressure waves hit your ear.

Projects Studio Handbook HARMONICS

This is a vibration plate. Sand collects in the areas which do not vibrate and create patterns. The patterns are called CHLADNI figures.

In fact, the sand collects in places where standing waves – waves that cancel each other out – form. The rest of the plate is vibrating and making the sound.

You will find more info about this violin shaped vibration plate here.

The frequency of the sound creating this Chladni pattern is shown in Hertz Hz (no. pressure waves per second that his your ear) is shown  for each pattern. (More about frequency in following posts)

Other Sound Math:

Make a match Box sing like Sinatra

The Curious Nature of Drummers’ Brains

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

h1

Sound Math 2: Can you hear this high pitch sound?

April 29, 2019

One of the best summaries of sound can be found here at Maths is Fun

Other Sound Math:

Make a match Box sing like Sinatra

The Curious Nature of Drummers’ Brains

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

h1

Sound Math 3: How loud is LOUD?

April 27, 2019

The logarithmic equation for sound and the decibel calculator here

More here

Other Sound Math:

Make a match Box sing like Sinatra

The Curious Nature of Drummers’ Brains

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

h1

Sound Math 4: Make a match Box sing like Sinatra

April 27, 2019

Other Mathspig Sound Posts:

The Curious Nature of Drummers’ Brains

Headbanger Maths

Pump Up the volume or Knock, Knock Knockin on Your skull wall!

h1

VAMPIRES: a math horror story

March 6, 2019

You will find TWILIGHT TV series Math here.

h1

Simple Equation For Calculating Skyscraper Sway in an Earthquake

October 2, 2018

A major and disasterous earthquake has just hit Indonesia. It is the job of engineers to calculate and incorporate – as far as possible- safety margins into the structures of buildings, dams, power plants and even pipe lines. Observers have noted that the skyscrapers in Fukushima wobbled during the recent 8.9 magnitude earthquake in Japan.


This is intentional, as rigid structures can snap in strong winds or during earthquakes.

But the maths used to calculate SKYSCRAPER SWAY is straightforward.

The Earthquake Engineering website offers a simple explanation.

Short, rigid buildings are damaged in earthquakes because they shake very fast. 10 story buildings have a period of oscillation of about 1 second the same as the earthquake pulse. This is VERY dangerous.

Tall, flexible buildings can withstand an earthquake because they can sway. They are like a very large, slow moving tuning fork. If they are TOO RIGID they snap. If they are too flexible the people on the 100th floor would be throw all over the place.

The 59-story steel-construction Citicorp Centre, NY (pictured) has an oscillation time of 6.7 seconds. Details Google Books.

The 102-story brick clad Empire State Empire Building sways about 8cm ( 3 inches) whereas the 110-story steel -mesh World Trades Centre Towers, NY, before they collapsed swayed over 1 m ( 3 ft 5 inches).

One more thing. You want buildings to have springy foundations so they don’t snap at the base and fall over.

Earthquake Engineering

The idea is not to strengthen the building, but to reduce the earthquake generated seismic forces acting upon it. This can be done in 3 ways.

1. Base Isolation. Rubber pads or Rollers. Are used so the base does not feel the full shake or jump off foundations.

Details Base Isolation Specialists

2. Shock absorbers or dampers are added to the structure to dissipate the seismic shock.

Details Damper Supplier

 

3. Active Tuned Mass Dampers use a computer controlled counter moving weight to actively move against the building sway.

The 508m (1,667-foot) Taipei 101 Tower would sway back and forth up to 60cm (2 feet) each way within five seconds. This according to Wired magazine is highly vomit inducing (barfomatic?).

The Taipei 101 engineers included a 662 tonne (730-ton) counter giant pendulum to act as a counter weight.Some buildings use a big block of concrete.

It is pushed in the opposite direction to the building sway to dampen the oscillation.

Earthquake Engineering Maths

Take 1:

Wired magazine includes the equation for Skyscraper Sway acceleration (See definition of terms @ Wired link):

But I’m going to use a student friendly equation from Wind Engineering for Large Structures.

Calculus Equation here.

Mathspigs, you can just look at this equation and see how to change it to make a building EARTHQUAKE SAFE. Keep in mind that k, the stiffness constant actually decreases for taller buildings.

Imagine you are designing a building to withstand the 8.9 magnitude earthquake. You have already added base isolation. Now you have three options to work with: building mass (m), damping constant (c) and stiffness constant (k). Remember the earthquake force is constant. If you change just the stiffness of the building (k) what happens to the distance of sway(x)?

Engineers have to come up with the optimum design for the strongest structure with least acceleration (but enough building mass for strength), greatest damping and least sway at the lowest cost.

h1

How far does the tallest buidling in the world SWAY in an earthquake?

October 2, 2018

Earthquake Engineering Maths

Take 2:

Structural Engineer Ron Klemencic explained on the Discover News that a simple rule of thumb for calculating skyscraper sway was to simply divide the buildings height in by 500 because the building codes demand the building fit a 1:500 sway ratio.

The tallest building in the world at 2,716 feet (828m), the Burj Khalifa, Dubai, would sway back and forth about 5.5 feet or 1.7 m.

Ahhhhhhhhh!  But you would have to drag Mathspig onto the 168th floor screaming.

But mathspigs you can work out the sway on the top ten tall buildings in the world.