The following table shows experimental measurements for the energy E (in J) for

Question

The following table shows experimental measurements for the energy E (in J) for different values of the velocity v (in m/s) for an object that is moving under a constant force F (in N): The mechanical relationships is given by: E = 0.5mv^2. i. Using interpolation, find E(v = 2.5 m/s) and v (E = 1000 J). ii. Using curve-fitting, find the best estimate for the value of the mass, m. iii. Plot a 1 times 2 graph, such that the first graph shows the measured and estimated values of E (on the y- axis) versus the v (on the x-axis), superimposed on top of each other, and the second graph shows a bar chart for the absolute estimation error (on the y-axis) versus the v(on the x-axis). iv. Find the velocity at which the measurement error for E was maximum.

Explanation / Answer

%interplotation between v and E for the desired curve fittings for the function is given to evaluate the following funciton .

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% Interpolation between V and E for best curve fittings

clc;
clear all;
disp('OUTPUT');
x=input('Enter the values of v in matrix format=');
y=input('Enter the values of E in matrix format=');
dy=input('Enter the values of dE/dV in matrix format=');
xp=input('Enter the value of V where E should be found=');
a=[1,x(1),x(1)^2,x(1)^3;1,x(2),x(2)^2,x(2)^2;...
0,1,2*x(1),3*x(1)^2;0,1,2*x(2),3*x(2)^2 ];
b=[y(1);y(2);dy(1);dy(2)];
n=length(b);
for i=1:1:n-1
for u=i+1:1:n % Partial Pivoting
if (abs(a(u,i))>abs(a(i,i)))
for v=1:1:n
temp=a(i,v);
a(i,v)=a(u,v);
a(u,v)=temp;
end
temp=b(i);
b(i)=b(u);
b(u)=temp;
end
end
end
for i=1:1:n-1
for k=i+1:1:n
factor=a(k,i)/a(i,i);
for j=1:1:n
a(k,j)=a(k,j)-factor*a(i,j);
end
b(k)=b(k)-factor*b(i);
end
end
for i=n:-1:1
s=0;
for j=i+1:1:n
s=s+a(i,j)*x1(j);
end
x1(i)=(b(i)-s)/a(i,i);
end
fprintf('The required Interpolating polynomial is- ');
fprintf('y=%.2f+%.2fX+%.2fX^2+%.2fX^3',x1(1),x1(2),x1(3),x1(4));
yp=x1(1)+x1(2)*xp+x1(3)*xp^2+x1(4)*xp^3;
fprintf(' At x=%f y=%f ',xp,yp);

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