What Should the Banking Angle Be to Prevent a Car from Sliding?

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    Car Friction
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The discussion focuses on determining the banking angle required to prevent a car from sliding off a banked curve. Key equations include the radial force balance and the vertical force balance, leading to the relationship between the banking angle, velocity, radius, and friction coefficient. The user has calculated the tangent of the angle but is struggling with two unknowns: the radius and the angle itself. They express confusion about conceptualizing the problem and seek guidance on how to approach finding the necessary angle to prevent sliding. The conversation emphasizes the importance of understanding the forces acting on the car in both radial and vertical directions.
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Homework Statement


phy.jpg


Homework Equations


\SigmaF=ma
ac=(v^2/r)
f = \muN

The Attempt at a Solution


\SigmaFradial= (radial-coordinate of normal force) + (radial component of friction) = ((mass)(velocity^2)/(radius))
\SigmaFy= (y-component of normal force) - (y-component of friction) = (mass)(gravity)

\SigmaFradial= Nsin\theta+\muNcos\theta = (mv^2/r)
\SigmaFy=Ncos\theta - \muNsin\theta = (mg)

I divided the equations for Fradial by the equation for Fy
and it yielded...

tan\theta = (v^2-\murg)/(rg+\muv^2)

so in order to find theta which I am looking for

\theta= arctan (v^2-\murg)/(rg+\muv^2)

but I have 2 unknowns...
we know
Vmax = 100km/h which is approx 27.78 m/s
g = 9.81 m/s^2 (this is given in the problem)
r= ?
\theta = ?
\mu= 0.22

also I am not sure how to conceptualize the part of the problem where i need to find out what theta needs to be to keep the car from sliding in the ditch.
I feel i can find the upper limit but not the lower. I thought about subbing something in for r to find theta but I'm stumped.
 
Last edited:
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what do you have so far? If nothing mathematical, what concepts are you thinking about?
 
im trying to get it to work, and the symbol stuff is screwing up.. how do i delete the post and start over?
 
Just start A new post I suppose.
 
okay i fixed everything, please help me out. The homework is already turned in, I just want the knowledge..
 
think about the x-direction of the normal force from the bank.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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