A reservoir dam has a vertical surface in contact with the water that is 125 m wide and 11.0 m high. Air pressure is one atmosphere. If the reservoir is completely filled, determine the magnitude of the net force acting on the dam. (Hint: Since the pressure varies linearly with depth, you will need to use your knowledge of calculus in order to determine the force on the dam due to water. Use 1.00 ✕ 103 kg/m3 for the density of water.)

The answer to the question is;

The net force acting on the dam is 73,001,115 N.

Explanation:

To solve he question, we note that

Pressure = Force/Area and the formula for pressure is

Pressure = hρg

While force, F= Pressure × Area

For a small area at the bottom of the dam we have

= hρg×dh×width

Where

w = width of the dam = 125 m

ρ = Density of water = 1.0×10³ m³

g = Acceleration due to gravity = 9.81 m/s²

h = Height  of the dam = 11.0 m

Therefore force over the dam wall =  =  

                                   = [ 11²/2×1×10³×9.81×125] - 0

                                = 73,001,115 N

The net force acting on the dam = 73,001,115 N.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day