dane: m₀ = 0,5 kg - masa ołowiu d₀ = 11 300 kg/m³ - gęstość ołowiu dt = 800 kg/m³ - gęstość tratwy dw = 1 g/cm³ = 1000 kg/m³ - gęstość wody szukane: Vt = ? - objętość tratwy Ciało pływa, gdy siła wyporu jest równa sile grawitacji. Fw = Fg [latex]F_{w} = d_{w}*g*V\V = V_{t}+V_{o} = V_{t}+frac{m_{o}}{d_{o}}\F_{w} =d_{w}*g*(V_{t}+frac{m_{o}}{d_{o}})[/latex] [latex]F_{g} = m*g\m = m_{t}+m_{o} = V_{t}*d_{t}+m_{o}\F_{g} = (V_{t}*d_{t}+m_{o})*g[/latex] [latex]d_{w}*g*(V_{t}+frac{m_{o}}{d_{o}})=(V_{t}*d_{t}+m_{o})*g /:g\\d_{w}*(V_{t}+frac{m_{o}}{d_{o}})=V_{t}*d_{t}+m_{o}\\V_{t}*d_{w}+frac{d_{w}*m_{o}}{d_{o}}=V_{t}*d_{t}+m_{o}\\V_{t}*d_{w}-V_{t}*d_{t}=m_{o}-frac{d_{w}*m_{o}}{d_{o}}\\V_{t}(d_{w}-d_{t}) = frac{m_{o}(d_{o}-d_{w})}{d_{o}} /:(d_{w}-d_{t})\\V_{t} = frac{m_{o}(d_{o}-d_{w})}{d_{o}(d_{w}-d_{t})}=frac{0,5(11300-1000)}{11300(1000-800)}=frac{5150}{2260000} =0,00227876106 m^{3}\\V_{t}approx2 279 cm^{3}[/latex]
