Imagine that it is possible to take a 4 kg mass and raise it straight up off the
ID: 1587902 • Letter: I
Question
Imagine that it is possible to take a 4 kg mass and raise it straight up off the Earth's equator on a huge tower that stretches beyond the Earth's atmosphere into space. If the top of the tower is 160.0 km directly above a point on the Earth's equator, what would the mass weight at the top of the tower? For comparison, on the surface of the Earth, the mass weighs 39.5 Newtons. DATA: Equatorial radius of the Earth 6.378E6 meters; mass of the Earth 5.98E24 kg; Gravitational Constant 6.673E-11 Nm^2/kg^2
Explanation / Answer
Newton’s law of gravitation states that the gravitational force between two masses goes as the square of the distance between them. For a 4 kg mass on the surface of the Earth,
r=RE,
the force is 19.7 N.
For the mass 160 km above the surface of the Earth,
r=RE+1.6X103 km. = 6.378x103+1.6X103 km =7.978x103 km
The force at 160 km then is
=rE2/(rE2+(1.6x105m)2)
=(7.978x103 km)2/((7.978x103 km)2+(0.16x103Km)2)
=63.64x106 km2/63.6656x106Km2
=0.9996
times the weight at the surface of the Earth, i.e
=mgh=4x9.8x1 (for 4 kg mass)
0.9996x(9.8x4)
=39.18 N
Calculation may be wrong but concept is right
times the weight at the surface of the surface of the Earth,i.e.0.95x19.7N