[单元] 重力场与重力位能
[来源] 100中兴 电机系
[题目]
A satellite moves in a circular orbit just above the surface of a planet,
assumed to offer no air resistence. If the satellite's orbit speed is v, the
escape velocity from the planet is
(A)v (B)(根号2)v (C)(根号3)v (D)2v (E)(2根号2)v
[想法]
我的想法是 总能E=U+K =-0.5U =-K K=(1/2)mv^2
所以 (1/2)m(脱逃速率)^2 -K =0 → 脱逃速率=v
但解答是
GMm/R^2=mv^2/R GM=Rv^2
再由力学能守恒
(1/2)m(脱逃速率)^2 -GMm/R = 0
→脱逃速率=(2GM/R)^1/2
代入前面求出的GM值 脱逃速率=(根号2)v