Question

A jet transport has a weight of 2.85 x 106 N and is at rest on the runway. The two rear wheels are 15.0 m behind the front wheel, and the plane's center of gravity is 11.8 m behind the front wheel. Determine the normal force exerted by the ground on (a) the front wheel and on (b) each of the two rear wheels.

Answer 1

here,

weight of the jet , w = 2.85 * 10^6 N

distance of the rear wheel from the from the front , dr = 15 m

distance of the centre of gravity from the from the front , dc = 11.8 m

a)

let normal force exerted by the ground on the front wheel be Nf

taking moment of force about the rear wheel

Nf * dr - w*( dr- dc) = 0

Nf * 15 - 2.85 * 10^6*( 15-11.8) = 0

Nf = 6.08 * 10^5 N

normal force exerted by the ground on the front wheel is 6.08 * 10^5 N

b)

let normal force exerted by the ground on each of the two wheel be Nr

taking moment of force about the front wheel

2*Nr * dr - w*(dc ) = 0

2 * Nr * 15 - 2.85 * 10^6*(11.8) = 0

Nf = 1.121 * 10^6 N

normal force exerted by the ground on the each rear wheel is 1.21 * 10^6 N