Resolving the Paradox: Net External Work in a Falling Ball-Earth System

[EzequielSeattle]

Homework Statement

Consider a system of a ball and the Earth. The ball is held at rest at an initial height, then dropped. Derive an expression for the net external work by external forces on BE.

Homework Equations

W = Fx
W = deltaK
V = mgh
K = (1/2)mv^2

The Attempt at a Solution

My confusion from this arises from the following: there are no external forces on the system. Therefore, the net external work of the system should be zero. However, the kinetic energy of the system changes and the potential energy decreases. Because the kinetic energy of the system increases, there should be work done because of W=deltaK. Clearly I'm guilty of a logical fallacy somewhere along the lines, but I'm unsure where.

 

[EzequielSeattle]

Just because I think this is intrinsically related: a hand pulls a block connected to a spring away from a wall to which the other end of the spring is attached. The initial and final velocity of the ball is zero. Kinetic energy doesn't change as a result. Is the work then zero?

I feel like I'm missing something fundamental here.

 

[Orodruin]

That no external work is done on the system does not mean that the system cannot redistribute its internal energy.