Why doesn't the gravity vector contribute to KE sliding down a ramp?

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Discussion Overview

The discussion revolves around the relationship between gravitational potential energy (PE) and kinetic energy (KE) for a block sliding down a ramp, particularly focusing on how the gravity vector contributes to the energy calculations involved in this scenario. The scope includes theoretical reasoning and mathematical formulation related to energy conservation and work done by forces.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that the kinetic energy at the bottom of the ramp can be expressed as KE = initial PE - any energy lost due to friction, implying that the work done by gravity is inherently accounted for in the change in potential energy.
  • Another participant proposes a more detailed equation for KE that includes the work done by the gravity vector, but questions whether this leads to double counting since the work done by gravity is already reflected in the change from initial to final potential energy.
  • A later reply suggests that solving the problem using both potential energy and work done by gravitational force could provide insights into why both methods yield the same result, indicating a potential exploration of the topic.

Areas of Agreement / Disagreement

Participants express differing views on how to account for the work done by gravity in energy calculations, with some arguing for a straightforward approach using potential energy changes, while others suggest that including gravitational work could lead to confusion about double counting. The discussion remains unresolved regarding the best method to approach the problem.

Contextual Notes

There is a lack of consensus on whether the work done by gravity should be explicitly included in the kinetic energy calculation or if it is already accounted for through changes in potential energy. The discussion also highlights potential confusion regarding the definitions and applications of work and energy in this context.

gazeem
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TL;DR
For physics questions where, say, a block is at the top of a declined ramp, how come the KE once the block reaches the bottom is determined by:

KE = initial PE - any energy lost due to friction

rather than:

KE = initial PE - any energy lost due to friction + any work done by the vector component of gravity that is parallel to the direction vector of the object.
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gazeem said:
KE = initial PE - any energy lost due to friction + any work done by the vector component of gravity that is parallel to the direction vector of the object
The PE is the same as the work done by the vector component of gravity that is parallel to the direction vector of the object.
 
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gazeem said:
Summary: For physics questions where, say, a block is at the top of a declined ramp, how come the KE once the block reaches the bottom is determined by:

KE = initial PE - any energy lost due to friction

Or more generally:
KE = (initial PE - final PE) - any energy lost due to friction

gazeem said:
rather than:

KE = initial PE - any energy lost due to friction + any work done by the vector component of gravity that is parallel to the direction vector of the object.
Beacuse that would be double accounting for the work done by gravity, which is already included as:
initial PE - final PE
 
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Ah okay I see. Thank you both so much for your responses, makes more sense now.
 
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gazeem said:
Ah okay I see. Thank you both so much for your responses, makes more sense now.

It would be a good exercise to solve the problem both ways: 1) using PE and 2) using W = Fd for the gravitational force down the slope.

This may give you an insight into why physically and mathematically they give the same result.
 
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