Question

A 3 -kg plastic tank that has a volume of \(0.2 \mathrm{m}^{3}\) is filled with liquid water. Assuming the density of water is \(1000 \mathrm{kg} / \mathrm{m}^{3},\) determine the weight of the combined system.

Short answer

Answer: To find the weight of the combined system, first calculate the mass of the liquid water: \(\text{mass of water} = 1000 \ \mathrm{kg/m^{3}} \times 0.2 \ \mathrm{m^{3}} = 200 \ \mathrm{kg}\) Next, determine the mass of the combined system: \(\text{mass of combined system} = 3 \ \mathrm{kg} + 200 \ \mathrm{kg} = 203 \ \mathrm{kg}\) Finally, calculate the weight of the combined system: \(\text{weight} = 203 \ \mathrm{kg} \times 9.81 \ \mathrm{m/s^{2}} = 1990.43 \ \mathrm{N}\) The weight of the combined system is approximately 1990.43 N.

Step-by-step solution

Find the mass of the liquid water

To calculate the mass of the liquid water, we will use the provided density and volume of the water: \(\text{mass} = \text{density} \times \text{volume}\) Using the formula, we can now compute the mass of the liquid water: \(\text{mass of water} = 1000 \ \mathrm{kg/m^{3}} \times 0.2 \ \mathrm{m^{3}}\)

Calculate the mass of the combined system

Now that we have the mass of the liquid water, we can determine the mass of the combined system by adding the mass of the plastic tank to the mass of the water: \(\text{mass of combined system} = \text{mass of tank} + \text{mass of water}\) \(\text{mass of combined system} = 3 \ \mathrm{kg} + (\text{mass of water})\)

Find the weight of the combined system

Weight is the force exerted on an object due to gravity. To find the weight of the combined system, we will use the following formula: \(\text{weight} = \text{mass} \times \text{gravitational acceleration}\) The value of gravitational acceleration is approximately \(9.81 \ \mathrm{m/s^{2}}\). Therefore, we can calculate the weight of the combined system as \(\text{weight} = (\text{mass of combined system}) \times 9.81 \ \mathrm{m/s^{2}}\). Now substitute the expressions from steps 1 and 2 to compute the weight of the combined system.