One kilogram of the explosive TNT supplies explosive energy of about 4.2×10^6 J. Let's see what that energy can achieve in lifting objects from Earth's surface to altitudes of hundreds of kilometers. We approach the issue through gravitational potential energy.
a. Assume the acceleration due to gravity is constant at g = 9.81 m/s2 from Earth's surface up to an altitude of 630 km above the surface. (A satellite at such an altitude would be in a "low Earth orbit.") What is the gravitational potential energy, in joules, of a 1.0-kg object at that altitude, taking the reference level for gravitational potential energy (U -0) at Earth's surface?
b. How many kilograms of TNT would need to be exploded, if the released energy were somehow used to raise a 10-kg object from Earth's surface to an altitude of 630 km at 100% efficiency, assuming constant g?
c. Again take the reference level at Earth's surface. Earth's radius and mass are 6.38x103 km and 5.97x1024 kg, respectively. Now calculate the gravitational potential energy, in joules, of a 1 0-kg object at an altitude of 630 km without assuming constant 25%
d. Without assuming constant g, how many kilograms of TNT would need to be exploded, if the released energy were somehow used to raise a 1-0-kg object from Earth's surface to an altitude of 630 km at 100% efficiency?