Conservation of Energy and the angle of the incline

AI Thread Summary
The angle of the incline does not affect how high a block will travel when pushed along a horizontal path and then released on a frictionless surface, as potential energy is solely dependent on height. The kinetic energy of the block can be fully converted to potential energy regardless of the incline's angle. However, if the transition from horizontal to incline is abrupt, some kinetic energy may be lost, impacting the block's ability to ascend. In cases of a sharp angle, such as a 90-degree transition, the block may come to a complete stop instead of climbing. A smooth, curved transition allows for the block to maintain its energy and continue upward.
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 hight. So I think the type of incline wouldn't matter in regards to the HIGHT 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 hight. So I think the type of incline wouldn't matter in regards to the HIGHT 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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