Question

A curve of radius 166 m is banked at an angle of 11°. An 736-kg car negotiates the curve at 81 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following. (a) the normal force exerted by the pavement on the tires.

Answer 1

Answer:

$F_n = 7509.33\ N$

Explanation:

given,

radius of curve = 166 m

angle of the banked road = 11°

mass of car = 736 Kg

speed of the curve = 81 km/h

                                = 81 x 0.278 = 22.52 m/s

normal force acting on the tires

on tire there will be two force acting on it

first one will be force acting due to weight and the other force acting on the tire is due to centripetal force.

$F_n = m g cos \theta+ \dfrac{mv^2}{r} sin \theta$

$F_n = 736 \times 9.8 \times cos 11^0+\dfrac{736 \times 22.52^2}{166} sin 11^0$

$F_n = 7080.28+429.047$

$F_n = 7509.33\ N$