Question

A 1600 kg car rounds a curve of radius 70 m banked at an angle of 12°. If the car is traveling at 84 km/h, will a friction force be required?

Yes friction force will be required, how much force?

Answer 1

Since we know that Friction force will be required, So

Using Force balance on Curve, to keep the car on the banked road:

Net force on car should be zero. So

Fnet = W + Ff - Fc = 0

Ff = Fc - W

Fc = Centripetal Force = m*V^2/R

W = Weight of car along the banked curve = m*a

a = g*sin theta

W = m*g*sin theta

Ff = Friction Force = ?

So,

Ff = m*V^2/R - m*g*sin theta

Using given values:

m = 1600 kg

V = 84 km/hr = 84*5/18 = 23.33 m/sec

R = radius of banked curve = 70 m

g = 9.81 m/sec^2

theta = 12 deg

So,

Ff = m*(V^2/R - g*sin theta)

Ff = 1600*(23.33^2/70 - 9.81*sin 12 deg)

Ff = 9177.5 N = Friction Force required

Please Upvote.