4.2.21 | revision #13278 | Savchenko Solutions

Statement

$$21.$$ ### Problem Statement

$$4.2.21^*.$$

a. A wooden cylinder with a radius of $1\mathrm{~m}$ and a height of $0.2 \mathrm{~m}$ rises to the surface from a depth of $$1$$ m in a body of water. The density of the wood is $0.8 \cdot 10^3 \mathrm{~kg/m^3}$ . How much heat will be released by the end of the motion of the water and the cylinder?

b*. A cylindrical plug with a radius of $$r$$ and a height of $$h$$ falls into a cylinder with a radius of $$R$$ , partially filled with liquid. The initial height of the lower surface of the plug above the liquid level is $$H$$ , and the initial velocity is zero. How much heat will be released by the end of the motion of the liquid and the plug? The density of the plug is $\rho$ , and the density of the liquid is $\rho_0 > \rho$ .

Solution

Answer

$\mathrm{a.~}Q=1\mathrm{~kJ.~b}^*.Q=\pi r^2\rho ghH\left[1+\frac{1}{2}\frac{h}{H}\frac{\rho}{\rho_0}\left(1-\frac{r^2}{R^2}\right)\right].$

Solution

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Answer

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