Potential Energy

Question

A 60.0kg person climbing a ladder to the moon.
a) Use EP = mgh to find your solution. Show all work.


b) Use EP = -GMm/r . Show all work.


c) Why do both methods disagree in this case?

Answer 1

I assume you want the potential energy due to just the earth's gravitational field.  

 

(a)

 

Since the gravity of earth is weakening as you rise in elevation, mgh will not give a correct potential energy U.  The rise in elevation is too large to use a constant g.  But here is what it gives:

 

h = earth-moon distance = 384.4 x 10⁶ m

 

U(h) = mgh = (60.0 kg)(9.81 m/s²)(384.4 x 10⁶ m) = 2.263 x 10¹¹ J

 

(b)

 

R = radius of earth = 6.371 x 10⁶ m

 

Evaluate the difference in U from the surface of the earth to the moon:

 

ΔU = U(R + h) - U(R) = -GMm/(R + h) + GMm/R = GMm[1/R - 1/(R + h)]

 

M = mass of earth = 5.972 x 10²⁴ kg

 

G = 6.67 x 10^-11 Nm²/kg²

 

ΔU = (6.67 x 10^-11)(5.972 x 10²⁴)(60.0)[1/(6.371 x 10⁶) - 1/(6.371 x 10⁶ + 384.4 x 10⁶] J

 

ΔU = (2.390 x 10¹⁶)(1.544 x 10^-7) J = 3.690 x 10⁹ J

 

(c)

 

See explanation provided in (a)