A circular swimming pool has a diameter of 16 m, the sides are 3 m high, and the depth of the water is 2.5 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8 m/s 2 and the density of water is 1000 kg/m 3 .)
I don't even know where to start!
To find the work required to pump all of the water over the side of the pool, we can start by calculating the volume of the pool.
1. Calculate the radius of the pool:
The diameter is given as 16 m, so the radius is half of that, which is 8 m.
2. Calculate the volume of the pool:
The pool can be thought of as a cylinder with a height of 3 m and a circular base with a radius of 8 m. The formula to calculate the volume of a cylinder is V = πr^2h, where π is a constant (approximated as 3.14159), r is the radius, and h is the height.
So, the volume of the pool is V = π(8^2)(3) ≈ 603.19 m^3.
3. Calculate the mass of water:
To calculate the mass of water, we need to know its density and volume. The density of water is given as 1000 kg/m^3, and the volume of water is the same as the volume of the pool, which is 603.19 m^3.
So, the mass of water is m = density * volume = 1000 kg/m^3 * 603.19 m^3 ≈ 603,190 kg.
4. Calculate the gravitational potential energy of the water:
To calculate the work required to pump the water out of the pool, we need to calculate the gravitational potential energy (GPE) of the water. The formula for GPE is GPE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height from which the water is lifted.
In this case, the height is the depth of the water, which is 2.5 m.
So, the gravitational potential energy of the water is GPE = 603,190 kg * 9.8 m/s^2 * 2.5 m = 14,824,715 J.
Therefore, approximately 14,824,715 Joules of work is required to pump all of the water over the side of the pool.