Cuprum

From the 1600 mm long sheet of copper plate 2 mm thickness, we have separated over the whole length of the belt weighing 6000 g. Calculate belt width if one dm³ copper weighs 8.9 kg.

Final Answer:

b =  210.7 mm

Step-by-step explanation:

$$\begin{gathered} a=1600\text{mm}\to \text{dm}=1600:100\text{dm}=16\text{dm} \\ h=2\text{mm}\to \text{dm}=2:100\text{dm}=0.02\text{dm} \\ m=6000\text{g}\to \text{kg}=6000:1000\text{kg}=6\text{kg} \\ \rho =8.9{\text{kg/dm}}^3 \\ m=\rho V=\rho abh \\ {b}_0=\frac{m}{\rho \cdot a\cdot h}=\frac{6}{8.9\cdot 16\cdot 0.02}=\frac{375}{178}\doteq 2.1067\text{dm} \\ b=b_0\to \text{mm}=b_0\cdot 100\text{mm}=2.1067\cdot 100\text{mm}=210.7\text{mm}=210.7\text{mm} \end{gathered}$$

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