Discworld has radius R and mass M; the incompetent wizard Rincewind has mass m and levitates at height h directly above the center of the disc. The gravitational force exerted by Discworld on the wizard is given by 2GMmh (1 F = 1 - R2 h (R² + h²)!/2 Assume h < R and think of F as a function of h, with the other quantities constant. (a) Expand F as a series in h/R. Give at least three nonzero terms. (b) Use your answer to part (a) to write a partial sum for the work required to move the wizard from h = 0.02R to h = 0.05R. Give at least three nonzero terms.

icon
Related questions
Question
Discworld has radius R and mass M; the incompetent wizard Rincewind has mass m
and levitates at height h directly above the center of the disc. The gravitational force
exerted by Discworld on the wizard is given by
2GMmh (1
F =
-
R2
h
(R² + h²)1/2
Assume h < R and think of F as a function of h, with the other quantities constant.
(a) Expand F as a series in h/R. Give at least three nonzero terms.
(b) Use your answer to part (a) to write a partial sum for the work required to move
the wizard from h = 0.02R to h = 0.05R. Give at least three nonzero terms.
Transcribed Image Text:Discworld has radius R and mass M; the incompetent wizard Rincewind has mass m and levitates at height h directly above the center of the disc. The gravitational force exerted by Discworld on the wizard is given by 2GMmh (1 F = - R2 h (R² + h²)1/2 Assume h < R and think of F as a function of h, with the other quantities constant. (a) Expand F as a series in h/R. Give at least three nonzero terms. (b) Use your answer to part (a) to write a partial sum for the work required to move the wizard from h = 0.02R to h = 0.05R. Give at least three nonzero terms.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS