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Projectile Motion: Accleration along an incline.

  • Thread starter lnjn
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Homework Statement


I don't need help with a homework question so much as a clarification of a concept. I realize that in projectile motion on a horizontal plane, horizontal acceleration is 0. But if an object is launched from the top of an incline (shaped like \), there is both an acceleration along the incline and one normal to the incline, right? The acc normal to the incline should be a = gcos(theta), and the acc along the incline should be a = gsin(theta).

I can see why the acc normal to the plane would become a = -gcos(theta), because the projectile is moving downward. But would the acc along the incline, gsin(theta) become negative as well, since in moving along the range of the incline, it is also moving at a downward angle? Would acceleration along the range be negative as well?

I was just confused because I used a neg acc for "normal" and a positive one for "along the plane," and the answer I received was the negative of the one I should have received. Thanks!
 

Answers and Replies

  • #2
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There is no acceleration normal to the incline. Think of what this would mean: when the object slides down an incline, it accelerates away from the incline, floating into the air. Obviously objects don't float into the air when they slide down a flat slope, so there is no acceleration normal to the incline.

You should try not to have the idea of a single free body undergoing multiple accelerations. Remember that acceleration is given by the equation:

[itex]\displaystyle a=\frac{F_{net}}{m}[/itex]

The important part being Fnet. There is a force that is normal to the incline, but the net force of an object sliding down an incline is always parallel to the incline. You should find the gravitational force and the normal force, and then add the vectors to find the net force. You can then find the acceleration using the above equation, with the net force vector you found.
 
  • #3
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Sorry, maybe I wasn't being clear.

The object isn't sliding down the incline, it's being launched into the air at a a certain angle ∅ at the top of the incline. This way, there would be two accelerations, yes?
 
  • #4
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For a body to accelerate, a net force must be applied.
In case of projectile, neglecting air resistance, the only force acting on a body is gravity which pointing downward.
So only vertical motion experience acceleration and none for horizontal component.
 
  • #5
CAF123
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For a projectile launched from an incline, if you set your axes such that x and y are parallel and perpendicular to the slope, then [itex] a_y = -g\cosθ [/itex] and [itex] a_x = g\sinθ. [/itex] The signs of these depend on your coordinate system. Here, I chose the positive direction of y to be perpendicular to the slope up away from the incline and x positive parallel to slope, acting downhill.
 

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