Applied Mathematics Teaser!

Michael Collins

Question 10, b(i), Higher 2008

See here: http://www.examinations.ie/archive/exampapers/2008/LC020ALP000EV.pdf

I have it worked out, but I can't seem to figure out how it works! I keep seeing a fatal flaw with my solution. Maybe I'm going mad...

So as not to influence your method I'll just let you have a go at it before telling you what I did.

Post the workings here if you can (so I can pick them apart!).

Cokehead Mother

Michael Collins

Ok, good - that's pretty much the way I did it. Now, here's the rub,

Power = dW/dt = d(Fs)/dt = F ds/dt = F v => P = F v when the force is constant.

In this case though, the force is not constant, at least we don't know that it is, so surely we have to use the more general form:

Power = dW/dt = d(Fs)/dt = F ds/dt + s dF/dt = F v + s Y*

We both used the simplier one in the solution since we said F = P/v.

So...how can it be right?

*I've used the term Yank for the time rate of change of Force...

Cokehead Mother

I think your definition of work (W = Fs) is the problem here.

If you were to say

then you'd end up with P(t) = F(t)v(t)

Michael Collins

Yep. That was it, a rookie mistake for sure!

So just to finish it off then it goes:

W = int (F.ds)

P = dW/dt = ds/dt dW/ds = v d/ds int(F ds) ...assuming force is along a straight line here, so by the fundamental theorem of calculus we get instantaneous power

P(t) = v(t) F(t) = F(t) v(t)

Cheers Cokehead.

steo87

Cokehead Mother wrote: »

Yeah....what he said.