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.

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## 2 Comments

## David Goodmanson (view profile)

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## Rachel Dawn (view profile)

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https://uk.mathworks.com/matlabcentral/answers/391130-trapezoidal-rule-to-find-total-work#comment_550827

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