A square pool with 100-m-long sides is created in a concrete parking lot. The walls are concrete 87 cm thick and have a density of 2.5 g/cm3. The coefficient of static friction between the walls and the parking lot is 0.42. What is the maximum possible depth of the pool? (The density of water is 1000 kg/m3.)

The horizontal pressure on the wall is densitywater*g*depth/2

The force of friction on wall is
mu*densityconcrete*depth*.87*100*g

setting these two equal
pressure*area=frictionforce
densitywater*g*depth/2*depth*100=mu*denstiyconcrete*g*depeth*.87*100

depth=2*.87*mu*densityconcrete/densitywater. check my math.

To find the maximum possible depth of the pool, we need to consider the equilibrium of forces acting on the walls of the pool.

First, let's calculate the mass of the walls. The volume of the walls can be calculated by subtracting the volume of the pool from the volume of the square formed by the outer edges:

Volume of the pool = (100 m)^2 x (maximum depth)
Volume of the square = (100 m + 2(0.87 m))^2 x (maximum depth)
Volume of the walls = Volume of the square - Volume of the pool

To calculate the volume of the walls in cubic meters (m³):
Volume of the square = (100 m + 2(0.87 m))^2
= (100 m + 1.74 m)^2
= (101.74 m)^2
= 10355.1076 m²

Volume of the pool = (100 m)^2 x (maximum depth)
Volume of the walls = 10355.1076 m² - 10000 m² x (maximum depth)
= 355.1076 m² x (maximum depth)

Now we can calculate the mass of the walls in grams (g):
Mass of the walls = Volume of the walls x Density of the walls
= 355.1076 m² x (maximum depth) x 2.5 g/cm³
= 887.769 g x (maximum depth)

To calculate the weight of the walls in Newtons (N):
Weight of the walls = Mass of the walls x Acceleration due to gravity
= 887.769 g x (maximum depth) x 9.8 m/s²
= 8,697.8952 g x (maximum depth) m/s²

Considering the equilibrium of forces, the maximum static friction force is given by:
Maximum Static Friction Force = Coefficient of Static Friction x Normal Force

The normal force is equal to the weight of the walls:
Normal Force = Weight of the walls
= 8,697.8952 g x (maximum depth) m/s²

Substituting the given coefficient of static friction:
Maximum Static Friction Force = 0.42 x 8,697.8952 g x (maximum depth) m/s²

Since the maximum static friction force is limiting the movement of the walls, it must balance the weight of the walls:
Maximum Static Friction Force = Weight of the walls

Therefore, we have the equation:
0.42 x 8,697.8952 g x (maximum depth) m/s² = 8,697.8952 g x (maximum depth) m/s²

To solve for the maximum depth, we can divide both sides of the equation by 8,697.8952 g:
0.42 x (maximum depth) m/s² = (maximum depth) m/s²

Dividing both sides of the equation by (maximum depth) m/s²:
0.42 = 1

Since 0.42 is not equal to 1, there is no maximum possible depth for the pool that satisfies the equilibrium condition. This means the walls would start to move before reaching any particular depth, and the pool cannot be built in this configuration.

To find the maximum possible depth of the pool, we need to consider the equilibrium of forces acting on the walls of the pool.

First, let's calculate the mass of the concrete walls.
Given:
- Dimensions of the pool: 100 m long sides
- Thickness of the walls: 87 cm
- Density of the walls: 2.5 g/cm3

We can calculate the volume of the walls using the dimensions of the pool. Since the pool is square, the volume can be calculated by multiplying the thickness by the surface area of the walls:
Volume of walls = thickness of walls * (2 * side length of pool + 2 * thickness of walls) * side length of pool

Plugging in the values:
Volume of walls = (87 cm) * (2 * 100 m + 2 * 87 cm) * 100 m

To convert the volume from cm3 to m3, we need to divide by 1,000,000:
Volume of walls = (87 cm) * (2 * 100 m + 2 * 87 cm) * 100 m / 1,000,000 = x m3

Next, we can calculate the mass of the walls using the density and volume:
Mass of walls = volume of walls * density of walls

Given:
- Density of the walls: 2.5 g/cm3
- Volume of the walls: x m3

Mass of walls = x m3 * 2.5 g/cm3

To convert the mass from grams to kilograms, we divide by 1000:
Mass of walls = x m3 * 2.5 g/cm3 / 1000 kg/g = x kg

Now that we have the mass of the walls, we can find the maximum possible force of static friction between the walls and the parking lot.

Given:
- Coefficient of static friction: 0.42

The force of static friction can be found using the equation:
Force of static friction = coefficient of static friction * normal force

The normal force is the force exerted by the walls on the parking lot, which is equal to the weight of the walls. The weight can be calculated using the equation:
Weight = mass * acceleration due to gravity

Given:
- Density of water: 1000 kg/m3

The volume of water required to fill the pool is equal to the volume of the pool (length * width * depth):
Volume of water = 100 m * 100 m * depth = y m3

The mass of water is then calculated by multiplying the volume with the density of water:
Mass of water = y m3 * 1000 kg/m3

Using the equation:
Weight = mass * acceleration due to gravity

Weight of water = y m3 * 1000 kg/m3 * 9.8 m/s2

To find the normal force exerted by the walls, we need to subtract the weight of the water from the weight of the walls:
Normal force = Weight of walls - Weight of water

Finally, we can find the maximum possible force of static friction:
Force of static friction = coefficient of static friction * normal force

To find the maximum possible depth of the pool, we need to balance the forces. The force of static friction should be equal to the weight of the water:
Force of static friction = Weight of water

We can rewrite the equation as:
coefficient of static friction * normal force = Weight of water

Plugging in the values we calculated earlier:
0.42 * (Weight of walls - Weight of water) = Weight of water

Solving for the maximum possible depth, y:
0.42 * (Mass of walls * acceleration due to gravity - y m3 * 1000 kg/m3 * 9.8 m/s2) = y m3 * 1000 kg/m3 * 9.8 m/s2

Simplifying and solving for y, the maximum possible depth of the pool.