1. A 670 kg meteorite happens to be composed of aluminum. When it is far from ea

Question

1. A 670 kg meteorite happens to be composed of aluminum. When it is far from earth, its temperature is -15 degrees Celsius and it moves with a speed of 14 km/s relative to the earth. As it crashes into the planet, assume that the resulting additional internal energy is shared equally between the meteor and the planet, and that all of the material of the meteor rises momentarily to the same final temperature. Find this temperature. Assume that the specific heat of liquid and gaseous aluminum is 1170 J/kgC.

2. The inside of a hollow cylinder is maintained at a temperature (Ta) while the outside is at a lower temperature (Tb). The wall of the cylinder has a thermal conductivity k. Ignoring end effects show the rate of energy conduction from the inner to the outer surface in the radial direction is:

dQ/dt =( 2(3.14)(L)(k)) (Ta-Tb/ln(b/a))

Explanation / Answer

The mass of the meteorite m = 670 kg The speed of the meteorite v = 14 km/s                                                = 14*10^3 m/s From law of cosnervation of energy, the loss in energy sue to crash            E = 1/2mv^2 + GMm/R = (0.5) (670 kg) (14*10^3 m/s)^2 + [(6.67*10^-11 Nm^2/kg^2) (5.98*10^24kg)(670kg) / 6.37*10^6 m]                = 6.566*10^10 + 4.195*10^10 = 10.761*10^10 J Since the energy shared equally between the mentor and the earth so the amount of energy gained by meteorite                       E = 5.38*10^10 J The inital temperature of the aluminum Ti = -15 deg The specific heat of aluminum C = 1170 J/kg C Then            Q = mcT              5.38*10^10 J = (670 kg) (1170 J/kg C) (Tf + 15)              68631 = Tf + 15 therefore the temperature              Tf = 68616 deg        

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