Discussions on answer of a problem

[neelakash]

I want to discuss the answers (what I get and what is given) of the following problem:

A particle slides down a smooth inclined plane of elevation θ,fixed in an elevator going up with an acceleration a.The base of the incline has a length L.Find the time taken by the particle to reach the bottom.

Working from an inertial frame I got the acceleration down the incline as (g-a) sinθ whereas working from elevator frame(non-inertial) one gets the acceleration down the incline as (g+a) sinθ.Why is there a difference?
Normally,when we see an object from outside an elevator and from the elevator,we se that the normal reaction force to be the same.So,what is making the difference?

 

[cesiumfrog]

You do know which equation doesn't contain a mistake, right?

 

[neelakash]

I think that there is some mistake that I am making.Otherwise the forces should be the same...
when I get it I will post that.

 

[cesiumfrog]

The second one is correct. Since the elevator is accelerating upward, the acceleration adds to gravity.

 

[neelakash]

The first answer is with respect to the ground.Show me that it is incorrect!

 

[cesiumfrog]

Because it is obviously unphysical for the solution to pass through zero as the upward acceleration increases.. The particle should slide faster, not turn around and go up the slope.

 

[neelakash]

Yes...I had done a mistake...
Now it is clear...