Minimum Force such that box m does not slide down

AI Thread Summary
The discussion revolves around calculating the minimum force required to prevent a smaller box (m) from sliding down a larger box (M) under the influence of gravity and friction. The calculations indicate that an acceleration of 49.05 m/s² is necessary for box m to remain stationary relative to box M, which is significantly higher than the provided acceleration of 2.0 m/s². Participants express confusion over the exercise's wording and the unrealistic nature of the given acceleration. Suggestions include assuming that the 2 m/s² is already present due to an unseen force, allowing for further calculations to determine the necessary horizontal force. The conversation highlights the need for clarity in physics problems to avoid misunderstandings.
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Homework Statement



slide.png

Homework Equations



F = ma; f = µN

The Attempt at a Solution


Let F' be the action-reaction force between box m and box M
f be the friction on small box m
For small box m:
F' = ma
f - mg = 0
µF' - mg = 0 since f = µF'
µma - mg = 0 since F' = ma
a = g / µ = 9.81 m/s2 / 0.2 = 49.05 m/s2
which is not equal to the given acceleration of 2.0 m/s2
Please help. Thanks



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Hello p, welcome to PF :smile:

This is a most peculiar exercise. What you calculate is correct: an acceleration of no less than 5g is required to make m stick to M with so much friction that it doesn't slide down. I find the exercise wording/picture combination very unsatisfactory: It isn't clear at all where the given 2 m/s2 comes from, and -- as you so justly put it -- 2 m/s2 is not 5g at all.

If an answer is absolutely required to get to the next level or something like that, then perhaps it's allowed to make some assumptions: for example that the 2 m/s2 is already there (some jet engine inside M that we can't see) and that the horizontal component of F is supposed to provide the remaining a' = 47.05 m/s2 to the ensemble of (m + M) . You apply Fx = (m+M) a' and some trigonometry to go from Fx to |F|.

Good luck, and maybe you can let us know what came out ?
 
Alright. Thanks! :)
 
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