I'm having some problem on my forces homework. Please help, I believe my answer is wrong, and I'm starting to get frustrated(adsbygoogle = window.adsbygoogle || []).push({});

Q: For a car traveling with speed 's' around a curve of radius 'r', determine a formula for the angle at which a road should be banked so that no friction is required to keep the car on the road. Then, find the angle for a curve of radius 50 m at a speed of 50 km/h.

I drew a Free Body diagram of an Inclined Plane, and the Circle the car is traveling. The following is my equations

NetForce(Y-direction)=Fn(ForceNatural) - Fgy(ForceGravity*Ydirection*) = 0

Nfy = Fn = Fgy

Nfy = Fn = Fg(Cos(Theta))

Nfc(Netforcecentrifical) = Ff(ForceFriction) = m(v^2)/r

Nfc = FnUs = m(v^2)/r

Nfc = Fg(Cos(Theta))Us = m(v^2)/r

Nfc = ma(cos(Theta))Us = m(v^2)/r mass cancels out

Nfc = a(cos(Theta))Us = v^2/r

Nfc = cos(Theta)Us = v^2/r(a) Us = V^2/r(a)

Nfc = cos(Theta) = (v^2)Us/r(a)

Nfc = Theta = cos^-1[(v^2)Us/r(a)]

Nfc = Thata = cos^-1[v^2(v^2)/ra(ra)]

Nfc = Thata = cos^-1[v^4/r^2(a^2)] <------ Final Equation

Nfc = Thata = cos^-1[50^4/50^2(9.8^2)]

Nfc = Theta = 89.9 Degrees <---- Final Answer

I think i did something terribly wrong, that answer doesnt seem right. Help would be very greatly appreciated...Thankz

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# Homework Help: Determine a formula for the angle at which a road should be banked

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