Why the energy value is constant?

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') 

Answer 1

[Walter Roberson]

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 = 

[MG NN]

i dont get the values by using the above coding. if i calculate manually my radius, mass get same answers with my original coding except for energy so how should i edit the line " g = zeros(size(X)); " ? so that i can plot the both the 2d graphs. thanks

[Walter Roberson]

format long g
I_n = sym(600);
W_n = sym(3000);
p_n = 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 = double(subs(Y, {x, I, W, p}, {X, I_n, W_n, p_n}))

y = 10×1

0.546301437541454 0.627535562636384 0.680544603101824 0.720849068502553 0.753748297474846 0.781740466085175 0.806216999664201 0.828038139190028 0.847775467872304 0.865829429391171

d = double(subs(D, {x, I, W, p}, {X, I_n, W_n, p_n}))

d = 10×1

4020.83784928201 3047.22526970439 2591.00384527135 2309.36491159003 2112.16848162765 1963.61372608496 1846.19403482264 1750.17132730742 1669.62737067591 1600.72437943207

g = double(subs(G, {x, I, W, p}, {X, I_n, W_n, p_n}))

g = 10×1

5400000000 5400000000 5400000000 5400000000 5400000000 5400000000 5400000000 5400000000 5400000000 5400000000

figure 
plot(y,g,'-*'), xlabel('Radius'), ylabel('Energy'), title('Energy vs Radius')

figure 
plot(d,g, '-*'), xlabel('Mass'), ylabel('Energy'), title('Energy vs Mass') 

The reason the plots are flat is that the equations you use are such that x cancels out.

Or at least it did with the equations you had posted before. You edited and removed the assignment to W so your code cannot run now.

[Walter Roberson]

For your revised equations:

Q = @(v) sym(v);

Pi = Q(pi)

Pi = 

π

I_n = Q(308)/10000

I_n = 

p_n = Q(7850)

p_n = 

7850

W_n = sym(3000)       %you did not initialize this so I used the previous value

W_n = 

3000

X = 1:1:10 ; 
syms I W p x positive

radius = (((2*I*x)/(p*Pi))^0.2)

radius = 

thickness = radius/x

thickness = 

mass = (p*(Pi*(radius*radius)*thickness))

mass = 

energy = ((mass)*((radius*radius)*(W*W)))/2

energy = 

Y = radius;
D = mass; 
G = energy;

y = double(subs(Y, {x, I, W, p}, {X, I_n, W_n, p_n}))

y = 1×10

0.0758 0.0870 0.0944 0.1000 0.1045 0.1084 0.1118 0.1148 0.1176 0.1201

d = double(subs(D, {x, I, W, p}, {X, I_n, W_n, p_n}))

d = 1×10

10.7289 8.1310 6.9137 6.1621 5.6360 5.2396 4.9263 4.6700 4.4551 4.2713

g = double(subs(G, {x, I, W, p}, {X, I_n, W_n, p_n}))

g = 1×10

277200 277200 277200 277200 277200 277200 277200 277200 277200 277200

figure 
plot(y,g,'-*'), xlabel('Radius'), ylabel('Energy'), title('Energy vs Radius')

figure 
plot(d,g, '-*'), xlabel('Mass'), ylabel('Energy'), title('Energy vs Mass') 

You can see that with your revised equations, still energy = I*W^2 for the same basic reason as before.

[MG NN]

So how should solve that since ur coding as shown above also produce the constant value?

[Walter Roberson]

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.