Two students are driving a Porsche of mass M at a constant speed,v, around a tra
ID: 1672297 • Letter: T
Question
Two students are driving a Porsche of mass M at a constant speed,v, around a traffic circle in front of an office building. Assumethat the road in the circle is level and has a radius R. Thecoefficient of friction between the car's wheels and the roadis .a). In terms of the quantities given, what is magnitude anddirection of the car's acceleration?
b.) At the instant when it passes directly in front of theoffice building, is there a net force on the car? If there is, whatis responsible for it and how big must it be? Express your answerin terms of the quantities given and explain your reasoning.
a). In terms of the quantities given, what is magnitude anddirection of the car's acceleration?
b.) At the instant when it passes directly in front of theoffice building, is there a net force on the car? If there is, whatis responsible for it and how big must it be? Express your answerin terms of the quantities given and explain your reasoning.
Explanation / Answer
a)Since the car doesn't move up or down (in the y axis) all theforces are balanced, that is weight and normal reaction. Therefore mg=N Friction(Ff) is equal to N=mg, and is the only forceproviding centripetal force required to move in a circle. Centripetal force = mv2/r mg=mv2/r v2/r=g also centripetal force is the net force acting on the body so usingF=ma, we get: mv2/r=ma a=v2/r =g towards thesignal (i.e inwards) b)The net force is only towards the center of the circle the car isnavigating. the magnitude is already given... Am i misunderstandingthis part ? EDIT: I think you can call it tangential velocity.. Since the caris not "accelerating" in any direction other than inwards(due tocentripetal acceleration), the net force is still zero.... Also, think about it this way.... We know there is accelerationtowards the centre of the circle.. This means that the forces donot have to balance eachother out.. So the "extra" force they areasking for is zero... Thats all i can think of right now...Hope that helped clear thingsup a bit..
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