Question

A jet transport has a weight of 1.87 x 10⁶ N and is at rest on the runway. The two rear wheels are 16.0 m behind the front wheel, and the plane's center of gravity is 12.0 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

a) R(fw) = 46.75*10⁶ (N)

b) R(rwi) = 70.125*10⁶ [N]

Explanation: See Attached file (the rectangle stands for a jet)

The diagram shows forces acting on the jet

Let R(fw) Reaction of front wheels and

R(rw) Reaction of rear wheels

Now we apply the Stevin relation, for R(fw) and a jet weight as follows

R(fw)/ 4 = 187*10⁶ / 16

Then :

R(fw) = ( 1/4) *187*10⁶ ⇒ R(fw) = 46.75*10⁶ (N)

And e do the same for the reaction on rear wheels

R(rw) / 12 = 187*10⁶ /16 ⇒ R(rw) =(3/4)*187*10⁶

R(rw) = 140,25*10⁶ [N]

The last expression is for the whole reaction, and must be devide by 2

because that force is exerted for two wheels, therefore on each of the two rear wheels the reaction will be:

R(rwi) = 70.125*10⁶ [N]