Answer :
Final answer:
The mercury's depth in the tank is found to be 7.53 inches. The total force on the larger side of the tank is 124.99 lb.
Explanation:
The question is about finding the depth of mercury in a tank and the total force on one of its sides. We can solve this using principles of fluid statics in Physics.
(a) The total force at the bottom of the tank is equal to the weight of the mercury in the tank. The weight of the mercury is calculated as the product of its volume and weight density. The volume of mercury is equal to the base area of the tank multiplied by its depth.
Thus, the total force (165lb) = volume of mercury * weight density of mercury (0.490lb/in³).
The base area of tank = length * breadth
= 5in * 9in
= 45 in².
Therefore, mercury's depth (h)= total force / (base area * weight density)
= 165lb / (45in² * 0.490lb/in³)
= 7.53in.
(b) The total force on the larger side of the tank will be the product of the pressure at the center of that side and its area. The pressure at the center is the weight density of mercury * (h/2), and the area is 9in * h.
So, the total force = 0.490lb/in³ * (7.53in/2) * 9in * 7.53in
= 124.99lb.
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