An empty 60 litre petrol tank has a mass of 10kg. Its mass when full of fuel of relative density 0.72 is

Physics

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Answer

53.2 kg\text{53.2 kg}

Step-by-step solution

4 steps

To calculate the mass of the tank when full of fuel, we need to find the mass of the fuel and add it to the mass of the empty tank.

  1. Convert the volume of the tank to cubic meters.

    The volume of the tank is V=60 litresV = 60 \text{ litres}.
    Since 1 litre=0.001 m31 \text{ litre} = 0.001 \text{ m}^3:

    V=60×0.001 m3=0.06 m3V = 60 \times 0.001 \text{ m}^3 = 0.06 \text{ m}^3
  2. Calculate the density of the fuel.

    The relative density of the fuel is 0.72.
    The density of water (ρwater\rho_{\text{water}}) is 1000 kg/m31000 \text{ kg/m}^3.
    Relative density is defined as the ratio of the density of a substance to the density of water:

    RDfuel=ρfuelρwater\text{RD}_{\text{fuel}} = \frac{\rho_{\text{fuel}}}{\rho_{\text{water}}}

    So, the density of the fuel (ρfuel\rho_{\text{fuel}}) is:

    ρfuel=RDfuel×ρwater\rho_{\text{fuel}} = \text{RD}_{\text{fuel}} \times \rho_{\text{water}} ρfuel=0.72×1000 kg/m3\rho_{\text{fuel}} = 0.72 \times 1000 \text{ kg/m}^3 ρfuel=720 kg/m3\rho_{\text{fuel}} = 720 \text{ kg/m}^3
  3. Calculate the mass of the fuel.

    The mass of the fuel (mfuelm_{\text{fuel}}) is its density multiplied by its volume:

    mfuel=ρfuel×Vm_{\text{fuel}} = \rho_{\text{fuel}} \times V mfuel=720 kg/m3×0.06 m3m_{\text{fuel}} = 720 \text{ kg/m}^3 \times 0.06 \text{ m}^3 mfuel=43.2 kgm_{\text{fuel}} = 43.2 \text{ kg}
  4. Calculate the total mass of the tank when full.

    The mass of the empty tank (memptym_{\text{empty}}) is 10 kg10 \text{ kg}.
    The mass of the tank when full (mfullm_{\text{full}}) is the sum of the mass of the empty tank and the mass of the fuel:

    mfull=mempty+mfuelm_{\text{full}} = m_{\text{empty}} + m_{\text{fuel}} mfull=10 kg+43.2 kgm_{\text{full}} = 10 \text{ kg} + 43.2 \text{ kg} mfull=53.2 kgm_{\text{full}} = 53.2 \text{ kg}

    The final answer is 53.2 kg\text{53.2 kg}.

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