A cone is filled w/ freshwater (w=62.4 lb/ft^3). Determine the total force on the inside of the cone. Height of 10 and base of 12.
The hydrostatic pressure is proportional to the height from the surface.
Force is pressure x area.
Net force is zero, since there is no movement.
Total force probably means the sum of all the scalar values of forces acting on the cylinder.
For this, you will need to integrate lateral forces over the surface of the cone, and add to the downward force acting on the base.
To determine the total force on the inside of the cone, we need to calculate the weight of the freshwater inside the cone using the formula:
Weight = Volume x Density x Gravitational acceleration
First, let's calculate the volume of the cone using the formula for the volume of a cone:
Volume = (1/3) x π x r^2 x h,
where r is the radius of the base and h is the height.
Given that the base of the cone has a diameter of 12, the radius (r) can be calculated as half of the diameter:
r = 12/2 = 6 ft.
We are given that the height (h) of the cone is 10 ft.
Now, we can substitute these values into the volume formula:
Volume = (1/3) x π x 6^2 x 10,
Volume = (1/3) x 3.14 x 36 x 10.
Simplifying this calculation, we have:
Volume = 376.8 ft^3.
Next, we can calculate the weight of the freshwater using the given density (w = 62.4 lb/ft^3):
Weight = Volume x Density x Gravitational acceleration,
Weight = 376.8 x 62.4 lb/ft^3 x 32.2 ft/s^2.
Now we can simplify this calculation:
Weight = 756,422.4 lb.
Thus, the total force on the inside of the cone, due to the weight of the freshwater, is approximately 756,422.4 lb.