(a) Derive an expression for the external work required to move a mass from a…

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

(a) Derive an expression for the external work

W

required to move a mass

m

from a distance

r_1

to a larger distance

r_2

(r_2>r_1)

from the centre of the Earth. (b) Show that when

h\ll R_{\oplus}

, your expression reduces to

W\approx mgh

, where

h=r_2-r_1

. (c) Using your result from part (a), calculate the work needed to raise a

100\,\text{kg}

package from the Earth’s surface to a height of

300\,\text{km}

. Use

R_{\oplus}=6.4\times10^{6}\,\text{m}

and

g=9.8\,\text{m s}^{-2}