A car travels around a 35 m radius unbanked curve. The static friction coefficient between the tires and the road is 0.45. What is the maximum speed at which the car can travel without slipping around this curve?
A) 2.8 m/s
B) 27.6 m/s
C) 12.4 m/s
D) 7.5 m/s

Question

Quizplus · Accepted Answer

The maximum speed at which the car can travel without slipping around the curve is determined by the centripetal force being equal to the maximum frictional force. The centripetal force is given by:

Fc = mv^2 / r

where:
m = mass of the car
v = velocity of the car around the curve
r = radius of the curve

The maximum friction force is given by:

Ff = μFn

where:
μ = friction coefficient
Fn = normal force

The normal force is equal to the weight of the car:

Fn = mg

Combining these equations, we get:

mv^2 / r = μmg

Solving for v, we get:

v = sqrt(μgr)

Plugging in the values, we get:

v = sqrt(0.45 x 9.8 x 35)

v ≈ 12.4 m/s

Therefore, the maximum speed at which the car can travel without slipping around the curve is approximately 12.4 m/s. Answer choice C is the correct answer.

A Car Travels Around a 35 M Radius Unbanked Curve