A small water tank which holds 5000 litres of water is filled with a pump in 10 minutes. The tank is 30m above the ground.
Calculate the increase in gravitational potential energy of the water.
PE=mgh
technically, if the bottom of the tank is at 30 meteres, the water had to be pumped higher, and you should use h as the location of the center of gravity for the water.
To calculate the increase in gravitational potential energy of the water in the tank, we need to use the following formula:
Potential energy (PE) = mass (m) × gravitational acceleration (g) × height (h)
First, let's calculate the mass of water in the tank. We know that the tank holds 5000 litres of water, and 1 liter of water has a mass of 1 kilogram (kg). Therefore, the mass of water in the tank is:
Mass (m) = volume × density
= 5000 litres × 1 kg/litre (density of water)
= 5000 kg
Next, we need to calculate the increase in height (h) of the water. Since the tank is 30 meters (m) above the ground, the increase in height is 30 m.
Lastly, we need to determine the value of the gravitational acceleration (g). On Earth, the standard value of gravitational acceleration is approximately 9.8 meters per second squared (m/s²).
Now we can substitute these values into the potential energy formula:
PE = m × g × h
= 5000 kg × 9.8 m/s² × 30 m
≈ 1,470,000 joules (J)
Therefore, the increase in gravitational potential energy of the water in the tank is approximately 1,470,000 joules (J).