A square pool with 180-m-long sides is created in a concrete parking lot. The walls are concrete 52.9 cm thick and have a density of 2.50 g/cm3. The coefficient of static friction between the walls and the parking lot is 0.515. What is the maximum possible depth of the pool?
I have never seen a question relating density and friction. I really don't know where to begin with this one. Any help or direction would be awesome.
No problem! I can help you break down the problem and guide you through it step by step.
To find the maximum possible depth of the pool, we need to consider two factors: the stability of the walls and the weight of the water.
First, let's consider the stability of the walls. The walls of the pool will exert a frictional force against the parking lot to prevent them from sliding. The coefficient of static friction between the walls and the parking lot is given as 0.515. This means that the maximum frictional force between the walls and the parking lot is equal to 0.515 times the normal force.
The normal force acting on the walls is equal to the weight of the water in the pool. To find the weight of the water, we need to find its volume and multiply it by its density. The formula for the volume of a square pool is V = side length x side length x depth.
The density of the walls is given as 2.50 g/cm3. To find their weight, we can multiply the volume of the walls (which is equal to the area of the pool times the thickness of the walls) by their density.
Now, let's put it all together:
1. Calculate the weight of the walls:
- Calculate the area of the pool: 180 m x 180 m = 32,400 m2
- Calculate the volume of the walls: 32,400 m2 x 52.9 cm = 1,709,160 cm3
- Convert the volume of the walls to cubic meters: 1,709,160 cm3 รท 1,000,000 = 0.00170916 m3
- Calculate the weight of the walls: 0.00170916 m3 x 2.50 g/cm3 = 4.27 kg
2. Calculate the weight of the water:
- Calculate the volume of the water: 180 m x 180 m x depth (m)
- Calculate the weight of the water: Volume of water x density of water (1,000 kg/m3)
3. Equate the maximum frictional force to the weight of the water:
- Maximum frictional force = coefficient of static friction x normal force
- Normal force = weight of the water
- Set the maximum frictional force equal to the weight of the water and solve for depth.
By following these steps, you should be able to find the maximum possible depth of the pool.