Question

(a) Taking the potential energy to be zero at infinite separation, find the potential energy of a 30 kg object at the surface of the Earth. (Use 6.37 ✕ 10⁶ m for the Earth's radius.)
________________J

(b) Find the potential energy of the same object at a height above the Earth's surface equal to the Earth's radius.
_______________J

(c) Find the escape speed for a body projected from this height.
__________________km/s

Answer 1

a)

Here is the formula for Gravitational Potential Energy

U_g = -GMm/r

U_g = - GMm/(R+h)

We plug given values,

U_g = - [(6.67*10^-11*5.9*10^24*30)/(6.37*10^6+ 0)

Calculating,

U_g = -1.85*10^9 J

b)

Now here h=R

U_g = - GMm/(R+h)

U_g = - [(6.67*10^-11*5.9*10^24*30)/(6.37*10^6+ 6.37*10^6)

Calculating,

U_g = -9.27*10^8 J

c)

To determine the escape velocity from this distance we just recall the usual method setting KE + PE = 0

1/2mv^2 = GMm/r

1/2,mv^2 = 9.27*10^8

1/2*30*v^2 = 9.27*10^8  

v= 7.8*10^3 m/s = 7.8km/s