Question

A piece of plastic barely floats in water if it has a mass of 20g, what is its volume

Answer 1

A piece of plastic barely floats in water if it has a mass of $20\mathrm{g}$, what is its volume

**Solution:**

$\mathrm{m} = 20\mathrm{g}$ – mass of the piece of plastic;

$\rho = 1\frac{\mathrm{g}}{\mathrm{cm}^3}$ – water density;

$\mathrm{F_a}$ – Archimedes force;

$\mathrm{V}$ – volume of the piece of plastic.

Newton’s second law for the piece of plastic on Y-axis:

$$\mathrm{mg} - \mathrm{F_a} = 0$$ $$\mathrm{mg} = \mathrm{F_a}$$ $$\mathrm{F_a} = \rho \mathrm{gV}$$

(2)in(1):

$$\mathrm{mg} - \rho \mathrm{gV} = 0$$ $$\rho \mathrm{gV} = \mathrm{mg}$$ $$\mathrm{V} = \frac{\mathrm{m}}{\rho} = \frac{20\mathrm{g}}{1\frac{\mathrm{g}}{\mathrm{cm}^3}} = 20\mathrm{cm}^3$$

**Answer:** volume of the piece of plastic is $20\mathrm{cm}^3$