Posts Tagged ‘equation’

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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.

 

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The Equation that tried to break the internet!!!

August 3, 2019

The following equation went viral on Twitter like the Yanni & Laurel sound Tweet. What answer do you get?

The Equation that tried to stump the internet! New York Times

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And the tic tic toc of the HYPERBOLA CLOCK

May 19, 2019

You will find everything you want to know about  HYPERBOLAS HERE.

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This is why students HATE algebra

January 31, 2019

So Mathspig is helping the kid next door with Grade 11 Math.

Here is the revision Q:

This is the sort of Q that makes students hate ALGEBRA. (Solution by Mathspig below)

POINTLESS

GRINDING

HEADACHE INDUCING

This equation looks like a chicken ran through some ink and ran across the page.

Why do so many MATH work sheets look like this?

The result:

THE ALTERNATIVE

One way to tackle a long and complexmath  problem is to defront the classroom and solve it in groups. 

ALGEBRA Q from HELL SOLUTION

Here is the Q in orginal form:

NOTE: With a proof, you have to prove that one side of the equation

equals the other.

 

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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.

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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.

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I Can’t Sleep: Caffeine Math Part 3 USA UNITS

August 14, 2018

I Can’t Sleep Math: Caffeine Maths METRIC HERE.

Sensitivity to caffeine varies for individuals, but in healthy adults the half life for caffeine is approx 6hrs meaning your body eliminates half the caffeine you have drunk in 6 hrs. Ref: Caffeine Pharmacology

Caffeine interferes with sleep. One study found that consuming caffeine 6 hours before bedtime reduced total sleep time by 1 hour.

Caffeine content sources Caffeine Content Data Base

Street art by JEKS, South Carolina

The Half life equation is an exponential function.

The Mayo Clinic advises up to 400mg Caffeine a day for adults, which would be;

10 black teas

7 instant coffees

4 cappuccinos

2 dark roast brewed

less than one cup of Black Insomnia Coffee.

Approx half this amount of caffeine for 14 yos.