Gravitational Potential Energy

Question

How much work would be done launching a 400 kg weather balloon to an altitude of 50 km?

 

I'm supposed to use the equation PE = Gm₁m₂(1/d_i - 1/d_f) but have no idea how this equation works

Answer 1

m₁ = mass of the earth (Look it up in kg.  It should be in your physics book.)

m₂ = mass of the balloon = 400 kg

d_f = distance from balloon at 50,000 meters to the center of the earth = (50,000 meters) + radius of earth

(Look up the mean radius of the earth in meters.)

d_i = distance from launch point of balloon to center of the earth = radius of the earth (since launched from surface of earth)

G = constant of universal gravitation (Look it up in your physics book in units of Nm²/kg²)

Plug the numbers into the formula you were given and get the work in units of joules.