(b) Show that the gravitational field is conservative by finding a potential P. Hence, verify the expression for work obtained in 5a. C, Figure 1: For question 5. The origin is at the centre of the Earth.
(b) Show that the gravitational field is conservative by finding a potential P. Hence, verify the expression for work obtained in 5a. C, Figure 1: For question 5. The origin is at the centre of the Earth.
Related questions
Question
Please solve (b)
Transcribed Image Text:5. In Newton's theory of gravitation, the Earth's gravitational field is given by,
-GM
r,
p3
g(F) =
|Fl, M is the mass of the
where r
= (x, y, z) is the position vector relative to the centre of the Earth, r =
Earth and G is the gravitational constant. The force acting on a particle of mass m at position 7 is given by
F = mg(r).
(a) A rocket of mass m is launched from position (0, 0, R) and travels to (0,0, R+ h) in a time T, along the
straight line path C1. A similar rocket travels along the spiral path C2 given by
)
2nt
7 = ñ(t) =
h
R+
T
2nt
- sin
0, cos
T
with 0 <t <T. By evaluating the appropriate line integrals, show that the work done by the gravitational
field along C1 equals the work done along C2 (Figure 1).
(b) Show that the gravitational field is conservative by finding a potential P. Hence, verify the expression for
work obtained in 5a.
C
C2
Figure 1: For question 5. The origin is at the centre of the Earth.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
