ul3 puints Previous Answers Tipler6 11.P.046 (a) Taking the potential energy to
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ul3 puints Previous Answers Tipler6 11.P.046 (a) Taking the potential energy to be zero at infinite separation, find the potential energy of a 14 kg object at the surface of the Earth. (Use 6.37 x 10 m for the 438314285.7 (b) Find the potential energy of the same object at a height above the Earth's surface equal to the Earth's radius. (c) Find the escape speed for a body projected from this height km/s In order for an object to just escape a gravitational field from a particular location, it must have enough kinetic energy so that its total energy is zero. eBook Submit Answer Save Progress] Practice Another Version ·0/1 points 1 Previous Answers Tipler6 11.P052. An object is projected upward from the surface of the Earth with an initial speed of 4.4 km/s. Find the maximum height it reaches [5265776.476 m y to relate the initial potential and kinetic energies of the object-Earth system to the final potential energy eBookExplanation / Answer
4)
for the potential energy
potential energy of the ball = - G* m * M/r^2
potential energy of the ball = -6.673 *10^-11 * 5.98 *10^24 * 14/(6.37 *10^6)
potential energy of the ball = -8.77 *10^8 J
b)
when the ball is at the height equal to radius of earth
potential energy of the ball = - G* m * M/(2r)^2
potential energy of the ball = -6.673 *10^-11 * 5.98 *10^24 * 14/(2 * 6.37 *10^6)
potential energy of the ball = -4.39 *10^8 J
c)
let the escape speed is v
as the total energy at infinite is zero
0.50 * m * v^2 - 4.39 *10^8 = 0
0.50 * 14 * v^2 - 4.39 *10^8 = 0
v = 7919 m/s = 7.92 km/s
the speed of the body projected is 7.92 km/s
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let the height reached is h
initial mechanical energy = final mechanical energy
-6.673 *10^-11 * 5.98 *10^24 * m/(6.37 *10^6) + 0.50 * m * (4400)^2 = -6.673 *10^-11 * 5.98 *10^24 * m/(6.37 *10^6 + h)
-6.673 *10^-11 * 5.98 *10^24/(6.37 *10^6) + 0.50 *(4400)^2 = -6.673 *10^-11 * 5.98 *10^24/(6.37 *10^6 + h)
solving for h
h = 1.16 *10^6 m
the maximum height it reaches is 1.16 *10^6 m
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