Kinetic Energy Gain: Why Is There a Difference?

[WiFO215]

Say a car is moving with speed u. The guy in the car chucks a ball with speed v relative to himself. The gain in KE,as recorded by him will be mv²/2. For an observer on the ground, i.e. non-moving frame, the change in kinetic energy is [(v+u)² - u²]m/2 = m[v² + 2uv]/2. Why is there a difference in energy gained? I am not able to put my finger on it.

 

[cesiumfrog]

Because there is a difference in how much the kinetic energy of the Earth and car has changed. (Do the math, imagine what happens when a roller-skater throws a brick.)

There was a long thread here previously about "DDWFTTW" propulsion, and your topic is the reason why it never made much sense there to argue (without agreeing on a reference frame) whether the cart's power was "coming from" either the air at the propeller or the ground at the wheels.

 

[Division]

I'm going to use the example Cesiumfrog used.

Think of a roller skater throwing a ball or a brick, the amount of energy the object thrown has is not just the energy that the roller skater threw the object, but also the momentum energy the roller skater had while he threw it