Answer
(a) $-5.5\times 10^8J$
(b) $-5.2\times 10^8J$
(c) $2.9\times 10^7J,3.0\times 10^7J$$
Work Step by Step
(a) We can calculate U at h=0 as
$U=-G\frac{M_Em}{R_E+h}$
We pug in the known values to obtain:
$U=-6.67\times 10^{-11}\times \frac{5.97\times 10^{24}(8.8)}{6.37\times 10^6}$
$U=-5.5\times 10^8J$
(b) At $h=350 Km$
$U_h=-G\frac{M_Em}{R_E+h}$
We plug in the known values to obtain:
$U_h=-6.67\times 10^{-11}\times \frac{5.97\times 10^{24}(8.8)}{6.37\times 10^6+350\times 10^3}$
$U_h=-5.2\times 10^8J$
(c) The difference is given as
$\Delta U=U_h-U$
$\Delta U=-5.50\times 10^8-(-5.21\times 10^8)$
$\Delta U=2.9\times 10^7J$
Now $\Delta U=mgh$
$\Delta U=8.8(9.8)(350\times 10^3)=3.0\times 10^7J$
