Motion of Orbiting Satellites AP Physics 1 FRQ – Exam Style Questions etc.
Motion of Orbiting Satellites AP Physics 1 FRQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Exam Style Practice Questions, Motion of Orbiting Satellites AP Physics 1 FRQ
Question
Two satellites, of masses m and 3m, respectively, are in the same circular orbit about the Earth’s center, as shown in the diagram above. The Earth has mass Me and radius Re. In this orbit, which has a radius of 2Re, the satellites initially move with the same orbital speed vo but in opposite directions.
a. Calculate the orbital speed vo of the satellites in terms of G, Me, and Re.
b. Assume that the satellites collide head-on and stick together. In terms of vo find the speed v of the combination immediately after the collision.
c. Calculate the total mechanical energy of the system immediately after the collision in terms of G, m, Me, and Re. Assume that the gravitational potential energy of an object is defined to be zero at an infinite distance from the Earth.
Answer/Explanation
Ans:
a. Fg = Fc gives \(\frac{GM_{e}m}{(2R_{e})^{2}} = \frac{mv^{2}}{2R_{e}}\) giving v = \(|\frac{\overline{GM_{e}}}{\overline{2R_{e}}}\)
b. conservation of momentum gives (3m)v0 – mv0 = (4m)v’ giving v’ = ½ v0
c. E = PE + KE = \(-\frac{GM_{e}(4m)}{2R_{e}}+\left ( \frac{1}{2}(4m)v^{2} \right )= – \frac{2GM_{e}m}{R_{e}}+2m\left ( \frac{1}{2} |\frac{\overline{GM_{e}}}{\overline{2R_{e}}}\right )^{2} = – \frac{7GM_{e}m}{4R_{e}}\)