Prob 1: How fast will an be falling when it hits the earth if it is dropped from a distance of 1.0 earth radius above the surface as shown? Use the conservation of energy approach. ME = 6.0 x 1024 kg and RE = 6.4 x 106 m. Step 2: Assume there is no funny business (ignore atmospheric effects.) Apply the conservation of mechanical energy. Use our newfound gravitational potential energy. Step 3: solve for vf. Note: your solution for vf will be the same as the speed of an object required for low earth orbit: vf = (GME/RE)^1/2. Is that what you found? Prob 2: What if you were to drop the apple in the problem above from an infinite distance away from the Earth? Find the impact speed on earth in this case. Follow the same careful steps you did in prob 1.
Prob 1: How fast will an be falling when it hits the earth if it is dropped from a distance of 1.0 earth radius above the surface as shown? Use the conservation of energy approach. ME = 6.0 x 1024 kg and RE = 6.4 x 106 m. Step 2: Assume there is no funny business (ignore atmospheric effects.) Apply the conservation of mechanical energy. Use our newfound gravitational potential energy. Step 3: solve for vf. Note: your solution for vf will be the same as the speed of an object required for low earth orbit: vf = (GME/RE)^1/2. Is that what you found? Prob 2: What if you were to drop the apple in the problem above from an infinite distance away from the Earth? Find the impact speed on earth in this case. Follow the same careful steps you did in prob 1.
UniversalGravitationalPotentialEnergy.docx