Mathematics for metal workers.espana netherlands

I shall try to tell in simple words some calculations with triangles what you have to know in a workshop.

Most people have problems with angle calculations. That’s the reason I starts with that subject.

Angle calculations

The base is a triangle with 1 angle of 90 degree ( angle C ).

The basic what you must learn is : SOT CAT TOA ( in English )

( En in het nederlands SOS CAS TOA )

When you know these words you can calculate every angle like this.

 

Sine = Oposite / The hypotenuse

Cosine =Adjacent / The hypotenuse

Tangent = Oposite / Adjacent

 

Example : CAT

This means :

    Cosine =Adjacent / The hypotenuse    

            Lets calculate.

                        Line AB = 4

                        Line BC = 2

            What is the angle of B ?

            We knows the Adjacent and the hypotenuse

 

            So , we use CAT

                        Cos ( B ) =  (Adjacent / the hypotenuse )

                        Cos ( B ) =  ( BC / AB )

                        Cos ( B ) =  ( 2 / 4 ) = 0.5

                        Angle of  B = inverse Cos( 0.5 ) = 60 degrees

 

Lengthcalculation

With Pythagoras.

Lets calculate.

                        Line AB = 5

                        Line BC = 3

Now we want to know what length is AC

 

It’s very simple.

           

            ( AB * AB )  =  ( AC * AC ) + ( CA * CA )

           

            AC * AC =  (AB * AB) – ( BC * BC )

            AC * AC =  ( 5 * 5 ) – ( 3 * 3 )

            AC * AC = 25 – 9 = 16

            AC = Root ( 16 )

            AC = 4

 

Weight Calculations.

An other kind of calculation is : What is the weight of a piece material.

When you want to know the weight op a piece of material , you must know what the volume is  multiply by the weight per litre.

Metal

aluminum

2,755

bismuth

9,8

bronze

8,2 ... 8,7

cast iron

7,2

gold

19,2

Iron (chem pure)

7,9

copper

8,6

plumb

11,3

magnesium

1,7

brass

8,4

nickel

8,8

wroughtiron

7,8

steel

7,6

tin

7,3

silver

10,5

zinc

7,0

synthetic

acrylic (fibre)

1,2

bakelite

1,30

synthetic (polyprop,PP)

0,91

Example.

           

            We have a piece of brass.

            Length = 200mm

            Diameter of  75 mm.

 

            Then the weight is :

                       

                        1 Litre = 1 dm3

                        that’s the reason why we calculate in dm.

                        200mm = 20cm = 2 dm

                        75mm = 7.5cm= 0.75dm 

 

                        Surface = ( PI * D * D ) / 4

                        Surface = ( 3.14 * 0.75 * 0.75 ) / 4

                        Surface =  0.4418 dm2

                        Volume = surface * length

                        Volume = 0.4418 * 2 = 0.8836 dm3

                        Weight per litre = 8.4

                        So this product weight 8.4 * 0.8836 = 7.42224 Kg