Solving Car Banked Problem: Friction Force at 88 km/h

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To determine the friction force required for a 1300 kg car rounding a banked curve at 88 km/h, the equations of motion must be analyzed. The vertical and horizontal forces are represented by the equations Fy = mg - Fn cos(12°) + Ffr sin(12°) = 0 and Fx = Fn sin(12°) + Ffr cos(12°) = mv²/r. The discussion highlights the need to isolate the frictional force (Ffr) and the normal force (Fn) using a system of equations. The user is advised to solve for one variable and substitute it into the other equation to find the required friction force. This approach will yield the necessary calculations to solve the problem effectively.
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A 1300 kg car rounds a curve of radius 70 m banked at an angle of 12°. If the car is traveling at 88 km/h, how much friction force is required?

ok so this is what i did so far but i got stuck.

the sum of Fy = mg - Fncos(angle) + Ffrsin(angle) = ma = 0
the sum of Fx = Fnsin(angle) + Ffrcos(angle) = ma = mv^2/r

i don't know how to get Ffr alone from here...help please!
 
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In your math courses this would have been called a system of equations. Your system here is 2 by 2 (2 equations, 2 unknowns). You can solve it by substitution. That is, solve for one of the variables in one of the equations, and then substitute the result into the second equation to eliminate one variable.
 
so are my two unknowns Ffr and a?
 
No, they are the frictional force and the normal force. You do know a.
 

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