Problem

A copper (Cu) weight is placed on top of a 0.50-kg block of wood (density = 0.60 × 103 kg/...

A copper (Cu) weight is placed on top of a 0.50-kg block of wood (density = 0.60 × 103 kg/m3) floating in water, as shown in Fig. 10–57. What is the mass of the copper if the top of the wood block is exactly at the water’s surface?

FIGURE 10–57

Step-by-Step Solution

Solution 1
Density of wood (ρW)=0.60 × 10³ kg / m³
Mass of wood (mw)=0.50 kg
Mass of copper + wood =M

At equilibrium, \(M g=B_{F}\)

$$ \begin{aligned} &\left(M_{\mathrm{cu}}+m_{\mathrm{w}}\right) g=m_{F} g \\ &=\rho_{F} V_{\mathrm{W}} \\ &M_{\mathrm{c} w}+0.50=10^{3} \times \frac{m_{\mathrm{w}}}{\rho_{\mathrm{W}}} \\ &=\left(10^{5} \times \frac{0.50}{0.60 \times 10^{5}}\right) \\ &M_{\mathrm{cu}}+0.50=0.833 \\ &M_{\mathrm{cs}}=0.33 \mathrm{~kg} \end{aligned} $$

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