Why the energy value is constant?

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MG NN
MG NN el 23 de Jun. de 2021
Comentada: Walter Roberson el 23 de Jun. de 2021
clear
clc
I=0.0308;
p=7850;
X=1:1:10 ;
y = zeros(size(X));
d = zeros(size(X));
g = zeros(size(X));
for i = 1:length(X)
x = X(i) ;
fprintf("\nWhen the ratio , x = %.1f", x)
radius=(((2*I*x)/(p*3.142))^0.2);
fprintf("\nThe radius is %.3fm", radius)
thickness=radius/x;
mass=(p*(3.142*(radius*radius)*thickness));
fprintf("\nThe mass is %.3fkg", mass)
energy=((mass)*((radius*radius)*(W*W)))/2;
fprintf("\nThe energy is %.3fW\n", energy)
y(i) = radius;
d(i) = mass;
g(i) = energy;
end
figure
plot(y,g,'-*'), xlabel('Radius'), ylabel('Energy'), title('Energy vs Radius')
figure
plot(d,g, '-*'), xlabel('Mass'), ylabel('Energy'), title('Energy vs Mass')

Respuestas (1)

Walter Roberson
Walter Roberson el 23 de Jun. de 2021
x cancels out.
radius involves x^(1/5)
Your energy calculation has radius*radius*thickness*radius*radius.
thickness = radius/x
So your energy calculation has radius*radius*radius/x*radius*radius . Which is radius^5/x . And since radius involves x^(1/5) that means radius^5 involves x^(1/5)^5 which is x . Which is then divided by x, giving something independent of x.
%I = sym(600);
%W = sym(3000);
%p = sym(7850);
X = (1:1:10).' ;
syms I W p x positive
Pi = sym(pi)
Pi = 
π
radius = expand(((2*I*x)/(p*Pi))^0.2)
radius = 
thickness = expand(radius/x)
thickness = 
mass = expand(p*(Pi*(radius*radius)*thickness))
mass = 
energy = expand((p*(Pi*(radius*radius)*thickness))*(radius*radius)*(W*W))/2
energy = 
Y = radius;
D = mass;
G = energy;
y = subs(Y, x, X)
y = 
d = subs(D, x, X)
d = 
g = subs(G, x, X)
g = 
  5 comentarios
MG NN
MG NN el 23 de Jun. de 2021
So how should solve that since ur coding as shown above also produce the constant value?
Walter Roberson
Walter Roberson el 23 de Jun. de 2021
I showed the symbolic calculations.
Your mass has radius*radius*thickness. Your energy has mass * radius*radius . Your thickness is radius/x . Multiply all those together and you have radius^5/x . Your radius has x^(1/5) and when you take that ^5 because of all the *radius then you get x^(1/5)^5 which is x^1 . Which is then being divided by x because of the thickness term. The end result is independent of x.
There are two possibilities here:
  1. That you made a mistake in the equations; or
  2. That the energy really is independent of x.
Verify that radius is proportional to x^(1/5) . If it is, then count how many times radius is multiplied together in creating energy. Then take into account any ratio between radius and x in creating thickness, that is also being multiplied to create energy. For the purpose of this calculation, you can ignore the actual value of all of the variables: you just need to look at powers of x being multiplied or divided together.

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