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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: aronno on October 27, 2009, 04:21:19 pm

Title: minimum maximum cases
Post by: aronno on October 27, 2009, 04:21:19 pm: i keep having trouble with these type of questions. these arent exactly the one where must differentaite but, other methods. (commonly used in forces questions) (i.e like find the mimimum angle etc.)

can anyone just jott a couple of situations and what to do in order to determine a minimum (something).
sorry if im being a bit vague.
Title: Re: minimum maximum cases
Post by: Mao on October 28, 2009, 12:17:53 am: This will generally involve solving inequality expressions. Such as an object mass M being pulled by a force P at an angle $\theta$ to the horizontal on a rough surface with coefficient of friction $\mu$

Then, $N + P \sin \theta = Mg \implies N = Mg - P \sin \theta$

Hence, for the object to move, $P \cos \theta - \mu N > 0 \implies P (\sin \theta + \mu \cos \theta) - \mu Mg > 0$

solving for $\theta$ will give the range of possible angles where the object will move, finding the minimum/maximum angle is just a matter of recognising the range of $\theta$ permitted.