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}