Question

A 1000-kg car travels along a straight 500-m portion of the highway (from A to B) at a constant speed of 10 m/s. At B, the car encounters an unbanked curve of radius 50 m. The car follows the road from B to C travelling at a constant speed of 10 m/s while the direction of the car changes from east to south. What is the magnitude of the frictional force (Centripetal force) between the tires and the road as the car negotiates the curve from B to C?

• A. 20 000 N
• B. 5000 N
• C. 2000 N
• D. 10 000 N

Answer 1

The correct option is C

2000 N

As the car is travelling at constant speed in a straight line, the acceleration is 0

Let:

v be the speed of the car on the curve,

r be the radius of the curve,

'a' be the car's acceleration towards the centre of the curve,

F be the friction force towards the centre of the curve which provides the necessary centripetal force

m be the mass of the car

Now, $a=\frac{v^2}{r}$

$=\frac{{10}^2}{50}$

$=2m/s^2$

$F=\frac{m{v}^2}{r}$

$=1000\times 2$

$F=2000N$