Answer to Question #160510 in Physics for Fifigrace

Question

Question 1

There is a bend in a level road (i.e. there is no camber) which has a radius of 25 m. The tyres on a vehicle are in good condition and the road is dry. In these circumstances the maximum frictional force is equal in magnitude to the gravitational force on the vehicle.

(a) What is the maximum speed at which the vehicle can go around the bend without skidding?

(2 marks)

There is black ice on the bend one morning, reducing the magnitude of the friction to 0.10 times the gravitational force on the vehicle.

(b) What is the maximum speed at which the vehicle can go around the bend on black ice without skidding?

Answer 1

a) The gravitational force provides the necessary centripetal acceleration, therefore we can write:

$$F_g=F_c,$$ $$mg=\dfrac{mv^2}{R},$$ $$v=\sqrt{Rg}=\sqrt{25\ m\cdot9.8\ \dfrac{m}{s^2}}=15.65\ \dfrac{m}{s}.$$

b) In this case, the force of friction provides the necessary centripetal acceleration, therefore we can write:

$$F_{fr}=F_c,$$ $$\mu mg=\dfrac{mv^2}{R},$$ $$v=\sqrt{\mu Rg}=\sqrt{0.1\cdot25\ m\cdot9.8\ \dfrac{m}{s^2}}=4.95\ \dfrac{m}{s}.$$