Hi a friend and I have a banked curve question that we would appreciate being walked through (; Detailed questiona nd diagram enclosed (;

Question

anonymous · Answer

1250 kg car rounds cruve with radius 72m banked at angle of 14 degrees. What amount of friction will be required and in what direction?

anonymous · Answer

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anonymous · Answer

maybe forces in x and y directions first?

anonymous · Answer

Sorry car is traveling 85 kph

anonymous · Answer

Yah, forces in x and y first.  Both x and y should equal 0 ^_^

anonymous · Answer

I think were suppose to find how much centripital force needed and then how much natural force we have first?

anonymous · Answer

The Normal force is what you find when you sum the forces in the y drection.  The centripetal is then equal to amount of friction - those are both in the x.

anonymous · Answer

ok

anonymous · Answer

I was wondering......

anonymous · Answer

I'm all astray.  Let me compose myself for a sec :P

anonymous · Answer

$$\sum fx= Ff - mgsin \theta - Fc$$

anonymous · Answer

That's what I had though, but I'm wrong.  That's with the x-axis pointing along the ramp, but centripetal acceleration points directly towards the center parallel to the ground.

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there's a vertical and horizontal component of both the normal force and friction if we align our axis like we would on a normal non-ramp p[roblem.

anonymous · Answer

I just found how to prove that this is not enough of an angle to not have friction so now need to find friction.

anonymous · Answer

$$\sum F_x = N \sin\theta + \mu _s N \cos \theta = Fc$$

anonymous · Answer

$$\sum F_y = - \mu _s N \sin \theta - mg + N \cos \theta = 0$$

anonymous · Answer

it's weird :P

anonymous · Answer

lol

anonymous · Answer

Then you can solve for friction.

anonymous · Answer

magic!

anonymous · Answer

Does that make sense (minus the magic)?:

anonymous · Answer

err, I guess when you saw that you needed friction was the velocity too great or too little?

anonymous · Answer

My tutoring skillz are abysmal tonight :P

anonymous · Answer

the velocity was to great, in order to to be frictionless we would need an angle of 38.3 degrees

anonymous · Answer

Then yah, the friction would need to be pointing towards the bottom of the ramp (do you see why?), so those equations are right ^^