Asked by Rachel Dawn
on 28 Mar 2018

I'm given 6 values for time, Force, and velocity. And I'm told to find total work with trapezoidal rule. (first time value is zero)

Does this seem correct? I excluded the code where I assign t=[0,#, #,...] & v=[.2, #, #...] & F=[2.0, #, #...]

pos(1)=0

work(1)=0

totalwork=0

for i=2:length(t)

area=(v(i)+v(i-1))*(t(i)-t(i-1))/2

pos(i)=pos(i-1) + area

work(i)= (pos(i) + pos(i-1))*(F(i)-F(i-1))/2

totalwork= totalwork + work(i)

end

totalwork

Answer by Roger Stafford
on 28 Mar 2018

Edited by Roger Stafford
on 28 Mar 2018

Accepted Answer

I would think your code should be this:

work = 0;

for k = 2:length(t)

work = work + (F(k)+F(k-1))/2*(v(k-1)+v(k))/2*(t(k)-t(k-1));

end

That is, the quantity "(v(k-1)+v(k))/2*(t(k)-t(k-1))" is the approximate displacement during the time interval t(k-1) to t(k), and if it is multiplied by the average force (trapezoid rule), "(F(k)+F(k-1))/2", during that time interval you would get the approximate work done then. The sum of the five work values should give you the total work done.

[Addendum: Or perhaps you could use this:

work = 0;

for k = 2:length(t)

work = work + (F(k)*v(k)+F(k-1)*v(k-1))/2*(t(k)-t(k-1));

end

because you are approximating the integral of F*v with respect to time, t.]

Rachel Dawn
on 28 Mar 2018

Hi Roger, Thank you! I checked this code and got a totally different answer for work then my previous code. What was wrong with mine, though?

Hmm. I just tried both those sections of code you included and they give different answers. I'm not sure why.

Update: I figured out what was wrong with my code! I had position as my bases & force as my height (should be the other way around). Thanks!

Roger Stafford
on 28 Mar 2018

" I just tried both those sections of code you included and they give different answers." Yes, they are not identical, but are different approximations. Assuming F and v vary in a reasonably smooth fashion, they should not be greatly different. It is the difference between

(F(k)*v(k)+F(k-1)*v(k-1))/2

and

(F(k)*v(k)+F(k)*v(k-1)+F(k-1)*v(k)+F(k-1)*v(k-1))/4

It is not clear which of these best represents the trapezoidal rule. I would hazard the guess that the first of these (that is, the second in the answer) is likely to be the best.

Sign in to comment.

Opportunities for recent engineering grads.

Apply Today
## 2 Comments

## David Goodmanson (view profile)

Direct link to this comment:https://de.mathworks.com/matlabcentral/answers/391130-trapezoidal-rule-to-find-total-work#comment_550490

## Rachel Dawn (view profile)

Direct link to this comment:https://de.mathworks.com/matlabcentral/answers/391130-trapezoidal-rule-to-find-total-work#comment_550827

Sign in to comment.