Conservation of Energy and the angle of the incline

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SUMMARY

The discussion centers on the conservation of energy concerning a block pushed with force F along a horizontal path before encountering an incline. It is established that the angle of the incline does not affect the maximum height the block can reach, assuming a frictionless surface and complete conversion of kinetic energy to potential energy. However, if the transition from horizontal to incline is abrupt, some kinetic energy may be lost, affecting the block's ability to ascend. A smooth transition mitigates this energy loss, allowing the block to maintain its kinetic energy more effectively.

PREREQUISITES
  • Understanding of kinetic and potential energy concepts
  • Familiarity with the principles of frictionless surfaces
  • Knowledge of inelastic collisions and energy loss
  • Basic grasp of incline mechanics and angles
NEXT STEPS
  • Study the equations for kinetic energy (KE = 1/2 mv²) and potential energy (PE = mgh)
  • Research the effects of friction on energy conservation in mechanical systems
  • Explore the dynamics of inelastic collisions and their implications in physics
  • Investigate the impact of incline angles on motion in various physical scenarios
USEFUL FOR

Physics students, educators, and anyone interested in understanding the principles of energy conservation and mechanics related to inclined planes.

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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