Projectile Motion: Accleration along an incline.

In summary, for a projectile launched from the top of an incline, there will be two accelerations: one along the incline (a_x = g\sinθ) and one normal to the incline (a_y = -g\cosθ). The signs of these accelerations depend on the chosen coordinate system. The net force of the object will be parallel to the incline, and the acceleration can be found using the equation a = Fnet/m.
  • #1
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!
 
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  • #2
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
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
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
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.
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air under the influence of gravity. It follows a curved path known as a parabola.

2. How is acceleration along an incline different from regular projectile motion?

In regular projectile motion, the acceleration is solely due to gravity. In acceleration along an incline, the object experiences both the force of gravity and the force of the incline, which can affect the direction and magnitude of the acceleration.

3. What factors affect the acceleration of an object along an incline?

The acceleration of an object along an incline is affected by the angle of the incline, the mass of the object, and the coefficient of friction between the object and the incline.

4. How do you calculate acceleration along an incline?

To calculate acceleration along an incline, you can use the formula a = gsinθ - μgcosθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), θ is the angle of the incline, and μ is the coefficient of friction.

5. Can the acceleration of an object along an incline be negative?

Yes, the acceleration of an object along an incline can be negative if the incline is steep enough and the coefficient of friction is large enough to cause the object to slow down as it moves up the incline.

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