To determine the force T required to raise the shield, we need to consider the hydrostatic forces acting on the shield. These include the buoyancy force exerted by the water on the shield, as well as the weight of the shield itself.
First, let's consider the buoyancy force. This is given by the formula:
Fb = ρ * g * V
where Fb is the buoyancy force, ρ is the density of water, g is the acceleration due to gravity, and V is the volume of water displaced by the shield.
To calculate the volume of water displaced, we can use the formula:
V = A * t
where A is the cross-sectional area of the shield and t is the height of the bottom hole.
The cross-sectional area of the shield can be calculated using the formula:
A = b * t * sin(a)
where b is the width of the shield and a is the angle of inclination.
Now that we have these formulas, we can plug in the given values to calculate the buoyancy force:
Fb = ρ * g * (b * t * sin(a) * t)
= 1000 kg/m^3 * 9.81 m/s^2 * (-6 m * 17.25 m * sin(40°) * 17.25 m)
= -398048.8 N
Next, let's consider the weight of the shield. The weight of the shield is given by the formula:
Fs = m * g
where Fs is the weight of the shield, m is the mass of the shield, and g is the acceleration due to gravity.
The mass of the shield can be calculated using the formula:
m = ρ * V
where ρ is the density of the shield material and V is the volume of the shield.
To calculate the volume of the shield, we can use the formula:
V = A * t
where A is the cross-sectional area of the shield and t is the height of the shield.
Now that we have these formulas, we can plug in the given values to calculate the weight of the shield:
Fs = ρs * (b * t * sin(a) * t) * g
= 7850 kg/m^3 * (-6 m * 17.25 m * sin(40°) * 17.25 m) * 9.81 m/s^2
= -3109093.9 N
Finally, to determine the force T required to raise the shield, we need to sum the buoyancy force and the weight of the shield:
T = Fb + Fs
= -398048.8 N + -3109093.9 N
= -3507142.7 N
Therefore, the force T required to raise the shield is approximately -3507142.7 N.