On a curved roadway of radius 100 m,the suggested speed limit is 35 mph (approximately 16 m/s).What must the coefficient of friction be between a car's tires and the road for the car to safely negotiate the curve at the posted speed?
A)0.72
B)0.51
C)0.26
D)0.40
E)0.13

Question

Quizplus · Accepted Answer

The centripetal force required to keep the car on the curve is given by F=mv²/r, where m is the mass of the car, v is its speed, and r is the radius of the curve. The force of friction between the tires and the road provides this centripetal force. The maximum friction force that can be exerted is given by the coefficient of friction μ times the normal force (the weight of the car in this case). Therefore, we have μmg=mv²/r, where g is the acceleration due to gravity. Solving for μ, we get μ=v²/(rg)=(16 m/s)²/[(100 m)(9.81 m/s²)]=0.26. Therefore, the coefficient of friction must be at least 0.26 for the car to safely negotiate the curve at the posted speed of 35 mph.

The best choice is C.

On a Curved Roadway of Radius 100 M,the Suggested Speed