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.)

Question

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.)

Answer 1

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Answer 2

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Answer 3

To find the maximum possible depth of the pool, we need to determine the maximum depth at which the weight of the concrete walls is balanced by the static friction force.

Let's start by calculating the weight of the concrete walls. The volume of the walls can be found by subtracting the inner square (with sides 100 cm shorter) from the outer square. The volume of the walls (V) is given by:

V = (10000 cm * 100 cm * 87cm) - (9800 cm * 100 cm * 87cm)

Next, we need to convert the volume to cubic meters by dividing by 1,000,000:

V = [(10000 cm * 100 cm * 87cm) - (9800 cm * 100 cm * 87cm)] / 1,000,000

Now, we can calculate the mass of the concrete walls by multiplying the volume by the density:

m = V * density

Given that the density of the concrete walls is 2.5 g/cm^3, we need to convert it to kg/m^3 by multiplying by 1000:

m = V * (density * 1000)

Now, let's calculate the weight (force) of the concrete walls:

W = m * g

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Next, we need to calculate the maximum static friction force (F_friction) using the coefficient of static friction (μ) and the normal force (N). The normal force is equal to the weight of the walls, which can be calculated as:

N = W

Finally, using the equation for static friction force:

F_friction = μ * N

we can calculate the maximum depth of the pool (h):

h = F_friction / (density_water * A)

where density_water is the density of water (1000 kg/m^3) and A is the area of the pool (length of one side squared).

Let's calculate each step:

1. Calculate the volume of the walls:
V = [(10000 cm * 100 cm * 87cm) - (9800 cm * 100 cm * 87cm)] / 1,000,000

2. Calculate the mass of the walls:
m = V * (density * 1000)

3. Calculate the weight of the walls:
W = m * g

4. Calculate the normal force:
N = W

5. Calculate the maximum static friction force:
F_friction = μ * N

6. Calculate the maximum depth of the pool:
h = F_friction / (density_water * A)

Now, you can plug in the values and calculate the maximum possible depth of the pool.