A rectangular concrete footing 2.0m long and 1.5m wide supports a vertical column. The total downward thrust transmitted by the column to the footing is 4.8×105N. During renovation, additional machinery is installed on the floor above, increasing the downward thrust on the same footing by 2.4×105N. The soil beneath the footing can safely withstand a pressure of only 2.0×105Pa.
(i) Calculate the pressure exerted on the soil by the footing before the installation of the additional machinery.
(ii) State, with justification, whether this initial pressure is within the safe bearing capacity of the soil.
(iii) After the additional machinery is installed, find the minimum area the footing should have so that the pressure on the soil does not exceed the safe limit.
(iv) If the width of the footing remains 1.5m, determine the new required length of the footing obtained in part (iii).