Water Bucket!

Classical Mechanics Level 2

A water bucket has a 10 10 -liter capacity when it is empty. If we put a 500 c m 3 \SI{500}{\centi\meter\cubed} piece of wood inside the bucket, then what is the volume of fresh water (in liters) that can fill the bucket?

Assumptions:

  • The density of fresh water is 1 g / c m 3 . \SI[per-mode=symbol]{1}{\gram\per\centi\meter\cubed}.
  • The density of wood is 0.7 g / c m 3 . \SI[per-mode=symbol]{0.7}{\gram\per\centi\meter\cubed}.


The answer is 9.65.

Ahmed Almubarak by Ahmed Almubarak , 38, Iraq

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1 solution

Denis Kartachov
Aug 22, 2018

The block will float in water because its density is lower than water, and the buoyant force will counteract its weight:

ρ H 2 0 V H 2 0 g = m w o o d g ⟹ V H 2 0 = ρ w o o d ρ H 2 0 V w o o d V H 2 0 = 0.7 1 ⋅ 500 = 350 c m 3 = 0.35 L \begin{array}{l} \rho_{H_20} V_{H_20} g = m_{wood} g \Longrightarrow V_{H_20} = \frac{\rho_{wood}}{\rho_{H_20}} V_{wood} \\ V_{H_20} = \frac{0.7}{1} \cdot 500 = 350 cm^3 = 0.35 L \\ \end{array}

Here V H 2 0 = 0.35 L V_{H_20} = 0.35L is the amount of water displaced by the block, so the bucket can only be filled by

V m a x = 10 − 0.35 = 9.65 L V_{max} = 10 - 0.35 = 9.65 L

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Great, please give the answer to two decimal places.

Ahmed Almubarak - 2 years, 9 months ago

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Oh sorry, I meant 0.35 not 0.3. I edited my solution

Denis Kartachov - 2 years, 9 months ago

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