An iron rocket fragment initially at - 100 ° C enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is 0 . 11 kcal kg - 1

Question

An iron rocket fragment initially at - 100 ° C enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is 0 . 11 kcal kg - 1 ° C - 1 , its melting point is 1535 ° C and the latent heat of fusion is 3 kcal kg - 1 . The minimum velocity with which the fragment must have entered the atmosphere is

TestHub · Accepted Answer

The kinetic energy of the fragment is changed to heat. Expressing mass m in kilograms everywher, we have

$\frac{1}{2} m v^{2} = [m (30) + m (0.11) (153 5^{\circ} + 10 0^{\circ})] 4184$

$v^{2} = (8368) [30 + 180] ≃ 1.76 \times 1 0^{6}$

Hence

$v = (\sqrt{1.76}) \times 1 0^{3} = {1.32 km s}^{- 1}$

Physics - Heat & Thermo Question with Solution | TestHub

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