Conservation of Energy and the angle of the incline

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Discussion Overview

The discussion revolves around the effects of the angle of an incline on the height a block can reach after being pushed along a horizontal path and then released on a frictionless surface. Participants explore concepts related to conservation of energy, potential energy, and the impact of the incline's angle on the block's motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the angle of the incline does not affect the height the block reaches, as the potential energy is dependent solely on height and not the path taken.
  • Others argue that if the incline transition is abrupt, kinetic energy may be lost, affecting the block's ability to climb the incline, particularly in cases of inelastic collisions.
  • A later reply suggests that a smooth transition from horizontal to incline would not introduce energy loss, implying that the angle would not matter in that scenario.

Areas of Agreement / Disagreement

Participants express differing views on whether the angle of the incline affects the height reached by the block, with some asserting it does not matter while others highlight potential complications due to abrupt transitions.

Contextual Notes

Participants assume a frictionless surface and discuss the implications of energy conservation without resolving the nuances of energy loss during abrupt transitions.

Sebastian B
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If I had a block that I pushed with a force F along a horizontal path and then removed the force before an incline, would the angle of the incline matter on how far above the ground the block would travel? I am assuming a frictionless surface.
 
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Sebastian B said:
If I had a block that I pushed with a force F along a horizontal path and then removed the force before an incline, would the angle of the incline matter on how far above the ground the block would travel? I am assuming a frictionless surface.
No.

Now what equations can you use to support this contention?
 
well since there is a certain kinetic energy in that block i am assuming if it would be converted completely to potential energy the path to get to that place wouldn't matter. The potential energy is only dependent on the height. So I think the type of incline wouldn't matter in regards to the height it would reach.
 
Sebastian B said:
well since there is a certain kinetic energy in that block i am assuming if it would be converted completely to potential energy the path to get to that place wouldn't matter. The potential energy is only dependent on the height. So I think the type of incline wouldn't matter in regards to the height it would reach.
That sounds right.

Because the surfaces are frictionless, there is no need to maintain a force on the block once it has reached the desired speed. (You said the block was being pushed with a steady force F. This means it will be constantly speeding up.)
 
There is one complication that can cause the angle to matter. If the transition from the horizontal to the incline is abrupt, some kinetic energy will be lost at the junction. If you require the object to remain in contact with the surface (a no-bounces requirement), this will be an inelastic collision. In the limit of a sharp 90 degree angle (e.g. between floor and wall), the object comes to an abrupt stop and does not climb the wall at all.

If the transition is curved rather than sharp then this effect does not intrude.
 

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