A concrete wall of thickness one metre of a dam can withstand a side pressure

of 10
5 2 N m-
. Find the thickness of sidewall at the bottom of the water dam at
a depth of 100 m. [ g =
- 10 m 2
s and density of water = 10
3
kg/m3
]

Well, let's dive right into it! We have a concrete wall trying to hold back some serious water pressure! To find the thickness of the sidewall at the bottom of the dam, let's start by calculating the pressure at that depth.

We can use Pascal's law, which states that pressure in a fluid increases with depth. Given that the density of water is 10^3 kg/m3 and the acceleration due to gravity is -10 m^2/s, we can find the pressure at a depth of 100 m.

Using the formula P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height, we can plug in the values:

P = (10^3 kg/m3)(-10 m^2/s)(100 m)

And voila! We find that the pressure at a depth of 100 m is... *drumroll* ... -10^6 N/m2.

Now, we know that the concrete wall can withstand a side pressure of 10^52 N/m, so we need to find the thickness of the sidewall that can withstand this pressure.

We can use the formula T = P x d, where T is the thickness, P is the pressure, and d is the depth. Plugging in the values:

10^5 N/m2 = -10^6 N/m2 x T

By doing a little math magic, we find that the thickness of the sidewall at the bottom of the water dam is... *trumpets please* ... 0.1 meters!

So there you have it! The thickness of the sidewall at the bottom of the water dam at a depth of 100 m is 0.1 meters. Keep that water in check, Mr. Dam!

To solve this problem, we can use the concept of hydrostatic pressure and the equation for pressure at a certain depth in a fluid.

1. First, let's calculate the pressure at the depth of 100 m using the equation:

P = ρgh

where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the depth.

Plugging in the given values:
ρ = 1000 kg/m³ (density of water)
g = -10 m/s² (acceleration due to gravity)

P = (1000 kg/m³) * (-10 m/s²) * (100 m)
P = -1,000,000 N/m²

2. Next, let's calculate the force exerted by the water on the sidewall at the bottom of the dam at this depth.

Force = Pressure * Area

As the wall is one meter thick, the area can be calculated as:

Area = length * height
Area = 1 m * 1 m
Area = 1 m²

Force = -1,000,000 N/m² * 1 m²
Force = -1,000,000 N

3. Finally, we can calculate the thickness of the sidewall at the bottom of the dam. Let's assume the thickness as x meters.

Given that the wall can withstand a side pressure of 1052 N/m, we can set up the equation:

Force = Pressure * Thickness

-1,000,000 N = 1052 N/m² * x

Solving for x:

x = -1,000,000 N / 1052 N/m²
x = -951.724 m

Since the thickness cannot be negative, we can conclude that the thickness of the sidewall at the bottom of the water dam at a depth of 100 m is approximately 951.724 meters.

To find the thickness of the sidewall at the bottom of the water dam, we need to determine the pressure exerted by the water at a depth of 100 m and then calculate the thickness using the given information about the pressure that the wall can withstand.

Let's start by calculating the pressure exerted by the water at a depth of 100 m. The pressure exerted by a fluid is given by the formula:

P = ρgh

Where:
P is the pressure (in pascals),
ρ is the density of the fluid (in kg/m^3),
g is the acceleration due to gravity (in m/s^2), and
h is the depth (in meters).

Given:
Depth (h) = 100 m
Density of water (ρ) = 1000 kg/m^3
Acceleration due to gravity (g) = -10 m/s^2

Using the provided values, we can substitute them into the formula to calculate the pressure P:

P = (1000 kg/m^3)(-10 m/s^2)(100 m)
P = -10^6 N/m^2

Now that we have the pressure exerted by the water, we can compare it to the maximum side pressure that the wall can withstand:

Maximum side pressure = 10^52 N/m^2

Since the pressure exerted by the water (-10^6 N/m^2) is less than the maximum side pressure that the wall can withstand, we can conclude that the wall can resist the pressure at the bottom of the dam.

To find the thickness of the sidewall at the bottom, we need to divide the pressure by the maximum side pressure and multiply by the thickness of the wall at the top. Let's assume the thickness of the sidewall at the top is 1 meter:

Thickness of sidewall at the bottom = (Pressure / Maximum side pressure) * Thickness of sidewall at the top
Thickness of sidewall at the bottom = (-10^6 N/m^2 / 10^52 N/m^2) * 1 m
Thickness of sidewall at the bottom = -10^-46 * 1 m
Thickness of sidewall at the bottom = -10^-46 m

However, a negative thickness doesn't make sense in this context. It seems there may be an error in the given values or calculations. Please check the values provided and the calculations, and if there are any discrepancies, correct them so we can proceed with the correct information.