Mathtotech-1

ref:Math&Tech/Joan Verdaguer i Codina, Ph.D.

Motiu d’aquest treball: En el curs d’Anglès fet a l’E.O.I. aquest juliol del 2007 dins del Pla de Millora, el professor Nick Bedford ens va demanar a cadascun fer una presentació per grups d’un tema en Anglès. Vaig escollir lligar un concepte de Matemàtiques que es fa servir a les classes de Tecnologia. Aquí hi ha la copia del que vaig explicar. Title: MATHEMATICS links to TECHNOLOGY In Mathematics is explained the equation of a (straight) line as y = a * x + b Other names: linear function function of the first degree Equation: y = a * x + b where y is variable x is variable a is a constant b is a constant and we say that

y varies as a function of x y is dependent on x y depends on x y depends upon x

if b = 0 then the origin of the line is in (0,0) and the equation is written as y = a * x the tan β is the slope of the straight line. remember that: β = tan-1 y/x, and when y = x then β = 45°

APLICATIONS in TECHNOLOGY SPRING The equation of a spring isF = k * x (see F as y; k as a; and x as x) where F is force [N] x is displacement [m] k is the constant of the spring the different values of k will give us different slopes, as for β = 30° the spring is soft (small F implies long x) for β = 60° the spring is strong (higher F implies short x) SOLID MECHANICS

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ref:Math&Tech/Joan Verdaguer i Codina, Ph.D.

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The equation of material resistance is: σ = Ε * ε

(see σ as y; Ε as a; and ε as x)

where: σ is stress [Pa] Ε is Young’s modulus, or elastic modulus (both terms mean the same) ε is strain [without units] you can say elastic limit or yield point at

.

The elastic behaviour is from the elastic limit

to x axis.

then tan β is elastic modulus or Young's modulus (both terms are accepted). for β = 30° the material is less resistant (for less σ we have long ε ; for example cooper, chewing gum) for β = 60° the material is more resistant (for less σ we have short ε ; for example iron, glass) ELECTRICITY The equation of Ohm’s law is V = R * I (see V as y; R as a; and I as x) where: V is voltage [V] R is resistor [Ω] I is intensity [A] Different slope of the line, means a low or high value of R, as for β = 30° R offers small resistance to pass electrons for β = 60° R offers high resistance to pass electrons THERMODYNAMICS (TEMPERATURE) To pass from Celsius degrees [°C ] to Fahrenheit degrees [°F ] we use the following equation °F = (9/5) * °C + 32 (see °F as y; (9/5) as a; °C as x; and 32 as b ) where °F is temperature in Fahrenheit degrees °C is temperature in Celsius degrees this case is interesting because the value of b is 32. It means that the origin of the line isn’t in the origin of the axes (0,0).