Question

An automobile weighing 1455 kg traverses a 458 m curve at aconstant speed of 48 kph. Assuming no banking on the curve, find the force acting on the tires necessary to maintain motion along the curve

Answer 1

Given:

An automobile weighing 1455 kg traverses a 458 m curve at a constant speed of 48 kph.

To find:

Force on the tires necessary to maintain the motion along the curved trajectory.

Calculation:

During travelling through the curved path the automobile would experience a outward centrifugal force which will try to take it off the road. But the frictional force will balance the centrifugal force and keep it on the road.

48 km/hr = 48 × (5/18) = 13.33 m/s.

Let required force be F ;

$\therefore \: F = \dfrac{m {v}^{2} }{r}$

$= > \: F = \dfrac{1455 \times {(13.33)}^{2} }{458}$

$= > \: F = \dfrac{1455 \times 177.7 }{458}$

$= > \: F = 3.17 \times 177.7$

$= > \: F = 564.52 \: newton$

So, force required is 564.52 N.