I can't work out c) for the following question, and I'd just like some help clarifying why my solution is wrong. Part a) and b) are fine.
A car rounds a bend on a road that follows the arc of a circle with radius 25.6 metres. The car has a mass of 885 kg and the force of kinetic friction between the tyres and the road is 9420 N
a) At what maximum speed should the car be moving so as to stay on the road?
b) Using Physics principles and your answer from above, quantitatively explain why motorists are advised to drive at slower speeds in wet weather.
c) If the bend in a) was banked at 8 degrees to the horizontal, show quantitatively how this increases the maximum speed that allows the car to remain on the road.
F(centripetal) = m*v^2 / r v^2 = 25.6*9420 / 885 = 272.4... v = 16.5m/s
In wet weather, friction is decreased. As
v = sqrt(v*F(c) / m), v will decrease if friction decreases. Hence, motorists must drive slower in wet weather to avoid slipping off the road.
See this image for a diagram of an inclined plane.
To find the coefficient of friction, we can say that
u = static friction / normal force. In this case,
static friction = mgsinθ and
normal force = mgcosθ.
u = tan(8) = 0.1405...
By equating formulas for centripetal force:
m*v^2 / r = u*m*g v^2 = 35.3 v = 5.94 m/s
Which is less than 16.5 m/s. I'm not sure where I went wrong, any help would be appreciated. Thanks.