Answer:
each door has a width of 2.666 meters
Explanation:
from Newton's second law applied to rotational motion:
ζ = I α
where ζ= torque , I = moment of inertia , α = angular acceleration
the moment of inertia for a flat plate around its central axis is
I = 1/12 m a² , where m= mass, a= total width = 2L
therefore the moment of inercia for a flat plate with length 2L ( 2 doors, one in each side of the central axis) is
I1 = 1/12 m (2L)² = 1/3 m L²
if we have 4 doors , that is 2 flat plates with length of 2L perpendicular to each other:
I = Ix + Iy = 2*I1 = 2/3 m L²
thus
ζ = I α
4* F * L = 2/3 * (4*m) L² * α
L = 3/2* F/ ( m*α) = 3/2* 56 N / ( 75 Kg * 0.420 rad/seg²) = 2.666 m
