Consider a rectangular swimming pool of depth 2.3 m with a width and length of 13 m. What is the force exerted by the water on one of the sidewalls of the pool?
the average depth is 2.3/2
the weight of water at that depth is the mass of water above, times g, times height..
weight of water at depth 2.3/2 m is
density water*g*volume water
1043kg/m^3*9.8N/kg*2.3m/2*1m^2
= 11753N
that is the average force on the wall
To find the force exerted by the water on one of the sidewalls of the pool, you can use the concept of pressure and the formula:
Force = Pressure × Area
Step 1: Calculate the pressure exerted by the water.
Pressure is defined as the force per unit area. In this case, the force is due to the weight of the water. The weight of an object can be calculated using the formula:
Weight = Mass × Acceleration due to gravity
The mass of the water can be obtained by multiplying its density with its volume. The density of water is approximately 1000 kg/m³.
Step 2: Find the area of the sidewall.
In this case, the sidewall of the pool is a rectangle. The area can be calculated as the product of the width and depth of the pool.
Step 3: Substitute the calculated values into the formula and calculate the force exerted.
Let's calculate it step by step:
Step 1: Calculate the pressure exerted by the water.
Density of water = 1000 kg/m³
Acceleration due to gravity = 9.8 m/s²
Volume of water = Length × Width × Depth
Volume = 13 m × 2.3 m × 2.3 m = 59.43 m³
Mass of water = Density × Volume
= 1000 kg/m³ × 59.43 m³
= 59430 kg
Weight of water = Mass × Acceleration due to gravity
= 59430 kg × 9.8 m/s²
= 582834 N
Step 2: Find the area of the sidewall.
Area = Width × Depth
= 13 m × 2.3 m
= 29.9 m²
Step 3: Calculate the force exerted.
Force = Pressure × Area
Pressure = Weight / Area
Force = (582834 N) / (29.9 m²)
≈ 19480 N
Therefore, the force exerted by the water on one of the sidewalls of the pool is approximately 19480 Newtons.