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Medals, Meglomaniacs and Sharp Shooters…….. The Math USA units

May 8, 2019

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question

‘Could medals protect the wearer from a sharpshooter?’ 

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

The target zone (circle) had a diameter of 0.7 inches. This is smaller than the diameter of an American Quarter, an Australian 10c and a UK pound all of which have a diameter of approx 0.96 inches.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.

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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!

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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!

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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!

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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!

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Which sport is more DANGEROUS to play? Cricket or baseball?

April 22, 2019

Reposted due to popular demand.

Mathspigs you are about to be hit on the head with some BALL PARK figures. There is so much maths involved in comparing cricket and baseball I hardly know where to begin. So I will just set you up with comparative statistics for starters. Here they are:

cricket and baseball stats mathspig

You now have sufficient information to calculate the following:

cricket 1_tnsQ1. If a cricket player  makes 4 runs (and runs between the wickets) and a baseball player hits a home run, who runs the furtherest?

ANS: 4 runs in cricket distance = 80.48 m

Home run in baseball distance = 109.6 m

Q2. What are the delivery ball speeds of an average pitcher and a mid paced bowler in m/sec?

ANS: Average Bowler Ball Speed = 110 – 125 km/h = 30.5 – 34.7 m/sec

Average pitcher Ball Speed = 80.47 km/h = 22.4 m/sec

Q3. How far would the delivery of an average pitcher and a  medium paced bowler travel in 10 seconds?

S = d/t

t = 10 secs:

d = S x t = S x 10

ANS: In 10 sec a ball bowled by an average bowler would travel 305 – 347 M

In 10 sec a ball thrown by an average pitcher would travel 224 m

baseball_01_tns Q4. If Shoaib Akhar fielded a ball in cricket 20 m from the wicket when the batsman was still 8m from the wicket (A typical running speed for humans is 32 km/h) would he be able to run him out?

Akhar ball speed S = 45.0 m/sec

d = 20 m

S = d/t

t = d/S

t  = 20/ 45.0

t = 0.44 secs

Batsman Speed = 32 km/h = 8.9 m/sec

How far can the batsman run in 0.44 secs?

d = S x t

d = 8.9 x 0.44 = 3.9 m

So batsman would be easily run out by Akhar as he is 8 m from the crease.

 Q5. How long would it take a ball thrown by Joel Zumaya to reach the batsman if the pitchers mound was exactly in the middle of the baseball square?

ANS: Speed of ball pitched by Zumaya = 168.65 km/h = 46.8 m/sec

Zumaya speed ball

shane warne cricketline

 

 

 Q6. Which sport is more dangerous?

We will base our calculations on the speed (or velocity) and the weight (or mass) of the ball. We must use the same units in all calculations. For each sport plot x-axis: velocity of ball (v) against y-axis mass x velocity (mv) of the ball. mv is the momentum. In ballistics the change in momentum is called the IMPULSE (impact for us). If you are hit on the head with a ball it is the change in momentum of the ball that does the damage. A small ball at a high speed can do as much damage as a larger ball at a slower speed. We are not including spin, curve balls or air resistance to keep calculations straight forward … literally!!! 

Cricket baseball ball IMPACT mathspig

cricket vs baseball impact mathspig

Now that you have your graph you can answer these questions:

tim_lincecum_101mphQ6a. Which sport for professional players is the most dangerous? 

You will have to look at the graph. A cricket ball is heavier than a baseball BUT the fastest pitchers can pitch a ball slightly faster than bowlers can bowl.  IMPACT (mv) depends on multiplying mass by velocity. You will see the stats for Akhar and Zumaya marked on the graph and you can use these stats to estimate impact.

BUT then there is the impact of batting, which increases the velocity of the ball. That will have to wait for another post.

Q6b. At what speed does a cricket ball do the same damage as a baseball? Give one example.  (Hint: Draw a straight line from the Y-axis)shoaib akhtar thaindian

Once again look at the  graph above!

You will find more maths on impact on Mathspig:  for a punch here and from hailstones here.

 

Pics: Tim Lincecum (Left) with 101 mph pitch, Shane Warne (Upper Right) and Shoaib Akhtar (Lower Left)

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Giant Easter Egg Math … USA units

April 5, 2019

Good News for Chocoholics

To get the right texture Easter Eggs are made from sugar or sucrose and not from corn syrup. But chocolate contains lots and lots of sugar.

Guylian sea shells

………………………………………………..

Guylian Sea Shells:

Weight Sea Shell: 4.23 oz

Weight Sugar: 1.69  oz

% sugar = 1.69/4.23 x 100 = 40%

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Guylian luxury easter egg

This is a Guylian Luxury Easter Egg. It can also be used as a designer handbag, I guess.

Guylian Easter Eggs:

Weight Easter Egg: 3.53  oz

Weight Sugar: 1.83 oz

% sugar = 1.83/3.53 x 100 = 52%

You’ll find nutrition data here.

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Easter Challenge:

You will find the largest Chocolate Easter Egg ever here.

This egg is 34 ft 1.05 in high and weighs 15,873lbs, but  it is ugly.

I like the GUYLIAN GIANT EGG (below) because it looks good and we know exactly how much sugar is in this egg. Mathspig Big Easter Egg

This Giant Egg was made in 2005 in Belgium by chocolate maker Guylian.

Statistics:

Height:  27 ft

Weight:  4300 lb Chocolate

No. Chocolatiers: 26

No. Chocolate bars: 50,000

Total time: 525 hrs

Easter Challenge for Chocoholics

fiat punto 1The amount of sugar in the giant egg weighs as much as a Fiat Punto.