moving block on a moving incline

Living_Dog

I have thought and thought about this problem for years and made no progress.

First off, the moving block on an incline plane has a simple solution using Newton's laws for both friction and no friction cases. But once the incline plane itself is allowed to move, on a frictionless surface, then my problem begins.

Now what I am asking for is someone to help me work through the solution rather than just handing me an answer. This is not for any homework. I saw it years ago (Taylor? Goldstein??) and have never thought of posting it here until now.


Thanks!

-LD
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ObsessiveMathsFreak

Let the incline have acceleration f, which for simplicity is parallel to the ground.

Now let the block have acceleration a relative to the incline. Note that this will be parallel to the slope of the incline.

However, the total acceleration of the block will be f+a. What this means is that the block will in fact accelerate into the plane of incline, so the component of its weight on the incline, minus the inclines reaction force will be nonzero. In other words, the reaction from the incline will not entirely cancel out the component of weight.

Note that the incline will have two forces on it. It's weight, and the reaction force from the block.

Now, draw a picture.

pam

Draw two separate FBD's.