Mass not sliding on a smooth, accelerating base

AI Thread Summary
To keep mass m stationary on a smooth, accelerating base M, the acceleration of M must equal g times the tangent of the angle of the incline (a = g tan(α)). The discussion emphasizes using Newton's second law to derive this relationship. The initial approach suggested calculating the acceleration of the block on a stationary ramp before considering the ramp's motion. While the derived answer is straightforward, other more complex solutions involving mass M exist. The consensus leans towards the simpler answer being appropriate for a quiz setting.
Karol
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Homework Statement


Mass m lays on the smooth triangle of mass M. what is the acceleration of M so that m will stay in place.

Homework Equations


Newton's second law: ##F=ma##

The Attempt at a Solution


$$\tan\alpha=\frac{ma}{mg}\;\rightarrow\; a=g\tan\alpha$$
 

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My suggestion is to determine the acceleration of the block if the ramp is not moving first, down the slope.
 
Looks right to me, is your answer supposed to be wrong?
 
Nathanael said:
Looks right to me, is your answer supposed to be wrong?
It's one of the possible answers but the other answers are complicated and include M. it's logical that my answer is correct since it's a short quiz, not a long exam
 

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