- #1
y90x
- 47
- 0
Homework Statement
If a curve with a tedious of 80m is perfectly banked for a car traveling 70km/h, what must be the coefficient of static friction for a car not to skid when traveling at 90 km/h ?
Homework Equations
Newton’s second law
F=ma
The Attempt at a Solution
To find the angle of the bank, I set the forces in the x-axis equal (because it’s perfectly banked In the first scenario) .
Fx = Fc
(Mg/cos(theta)• sin theta)=mv^2 / r
Mass cancels out
So we’re left with
g• (sin theta / cos theta) = v^2 /r
Sin over cos equals to tan , so
gtan theta = v^2/r
Isolate theta and you get
Theta = tan^-1 (v^2/r)
Theta = than^-1 (19.5^2/80)
Theta= 25.8
I will insert a photo of my free body diagram so it won’t seem confusing and my work just in case .
To find the static friction :
We can conclude that
Fnsin(theta) + Fcos(theta) =mv^2/r
And
Fncos(theta)= mg
So we isolate fn from the second equation and plug in into the first equation
So ..
(Mg/cos(theta))•sintheta + (mu)(mg/cos theta) • cos theta = mv^2/r
Simplify it to :
gtan(theta) + (mu)gcos theta= v^2/r
Isolate mu
Mu=[(v^2/r)-gtan theta]/gcos theta
When you plug in the numbers it’ll look like this
Mu= [(25^2/80)-9.8tan(25.8)]/9.8cos(25.8)
I keep getting
Mu= 0.345
The correct answer should be 0.2275
Where did I go wrong or did I miss a step ?https://www.physicsforums.com/attachments/216722
Last edited: