A flat (unbanked) curve on a highway that has a radius of 50 m. A car rounds the curve. The car has mass 4,907 kg. The static coefficient of friction between the curve and the car is 0.35. What is the maximum speed of the car to prevent sliding?

maximum speed of the car to prevent sliding is 13.1m/s

Explanation:

Given data

Radius of curve r=50m

Mass of car m=4907kg

Coefficient of friction u=0.35

Limiting for R=?

Hence limiting force R=ma

R=4907*9.81

R=48137.7N

We know that the force to overcome friction is

F=uR

Hence

F=0.35*48137.7

F=16848.2N

Centripetal force along the curve is given as

Fc=mv²/r

Fc = centripetal force

m = mass

v = velocity

r = radius

To solve for velocity we have to equate both force required to overcome friction and the centripetal force

Fc=mv²/r=F=uR

mv²/r=uR

Making velocity subject of formula we have

v²=u*r*R/m

v² = (0.35*50*48137.7) / 4907

v²=842409.75/

v²=171.67

v=√171.67

v=13.1m/s