Kinetic Energy Gain: Why Is There a Difference?

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SUMMARY

The discussion centers on the differences in kinetic energy gain when an object is thrown from a moving vehicle, specifically a car. When a ball is thrown with speed v relative to the car, the kinetic energy gain observed by the thrower is calculated as mv²/2. In contrast, an observer on the ground measures the change in kinetic energy as m[v² + 2uv]/2, highlighting the importance of the reference frame in energy calculations. This discrepancy arises due to the combined effects of the thrower's initial momentum and the relative motion of the car.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly kinetic energy
  • Familiarity with reference frames in physics
  • Basic knowledge of momentum and energy conservation laws
  • Ability to perform algebraic manipulations for kinetic energy equations
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  • Explore the concept of reference frames in physics
  • Study the principles of momentum conservation in collisions
  • Investigate the implications of kinetic energy in different frames of reference
  • Learn about real-world applications of kinetic energy calculations in automotive physics
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This discussion is beneficial for physics students, educators, and anyone interested in understanding the nuances of kinetic energy and reference frames in motion analysis.

WiFO215
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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.
 
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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.
 
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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
 

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