the mechanical work W done in using a force F to push a block through a distance
ID: 2083627 • Letter: T
Question
the mechanical work W done in using a force F to push a block through a distance D is W=F.D. The following table gives data on the amount of force used to push a block through the given distance over five segments of a certain path. The force varies because of the differing friction properties of the surface. Write a function file subprogram to find a) the work is done on each segment of the path.
b) the total work was done over the entire path.
Path Segment
1
2
3
4
5
Force (N)
400
550
700
500
600
Distance (m)
2
0.5
0.75
1.5
3
Path Segment
1
2
3
4
5
Force (N)
400
550
700
500
600
Distance (m)
2
0.5
0.75
1.5
3
Explanation / Answer
clc clear all close all syms x y z t F=input('Enter the force components in cartesian co ordinates: '); C=input('Enter the parametric form of curve C(t): '); L=input('Enter the limits of parameter L: '); T=linspace(L(1),L(2),101); X=(subs(C(1),t,T));%x-coponent of c(t) Y=(subs(C(2),t,T));%y-component of c(t) xL=[min(X)-0.2,max(X)+0.2];%setting up x-limits for plotting purrpose yL=[min(Y)-0.2,max(Y)+0.2];%setting up y-limits for plotting purrpose if numel(F) ==2 FF=subs(F,{x,y},C);%calculating F(C(t)) for use in line integral vect2D(F,xL,yL);hold on;%calling vect2D function to draw vector field plot(X,Y,'-r','LineWidth',2)%plotting the curve C elseif numel(F)==3 FF=subs(F,{x,y,z},C); Z=(subs(C(2),t,T)); zL=[min(Z)-0.2,max(Z)+0.2];%setting up z-limits for plotting purrpose vect3D(F,xL,yL,zL);hold on;%calling vect3D function to draw vector field plot3(X,Y,Z,'-r','LineWidth',2);%plotting the curve C else disp('Function entered is not 2D or 3D vwctor field'); return end axis on; xlabel('x') ylabel('y') zlabel('z') intgrnd=inline(vectorize(dot(FF,diff(C,t))),'t'); WD=quad(intgrnd,L(1),L(2)); disp(['the work done by the force field is: ',num2str(WD)]);
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