- #1
Hendrick
- 43
- 0
Homework Statement
A car goes around a curved stretch of flat roadway of radius R = 104.5 m. The magnitudes of the horizontal and vertical components of force the car exerts on a securely seated passenger are, respectively, X = 236.0 N and Y = 572.0 N.
This stretch of highway is a notorious hazard during the winter months when it can be quite slippery. Accordingly the DMV decides to bank it at an angle φ = 23.5 ° to the horizontal.
(1) What is the maximum speed at which the car could safely negotiate this banked curve during a wintry night when the coefficient of static friction between the road and tyres is μs = 0.24 ?
Homework Equations
F_s = (m*v^2)/r
F_s = μ_s * n
n = m*g
where n is the normal force and μ_s is the coefficient static friction.
The Attempt at a Solution
v = ((F_s*r)/m)^1/2
v = ((μ_s*n*r)/m)^1/2
v = ((μ_s*m*g*r)/m)^1/2
v = (μ_s*g*r)^1/2
v = (0.24*9.81*104.5)^1/2 * 3.6 (to convert ms^-1 to kmh^-1)
= 56.5 kmh^-1 (3sf)
Actual answer is 100 kmh^-1 (to 3sf)