Which box will start to slide first?

AI Thread Summary
The discussion revolves around predicting which of two boxes, weighing 10kg and 20kg, will slide first when a plank is tilted. It was determined that both boxes will begin to slide at the same angle of 21.8 degrees, despite their weight difference. This counterintuitive result arises because the forces acting on each box are proportional to their respective weights, leading to a cancellation effect. The angle of sliding is independent of mass and solely dependent on the coefficient of static friction. The conclusion confirms that the static friction coefficient dictates the sliding angle, not the weight of the boxes.
Kelsob
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Homework Statement


A crane is raising a plank carrying two boxes that only differ in weight. The boxes weigh 10kg and 20kg respectively. As the plank tilts toward the heavier box, predict which box will start to slide first. Explain your prediction.

Homework Equations



Coefficient of static friction = Force of static friction / Normal Force.

The Attempt at a Solution



From my attempts at solving with a randomly assigned coefficient of static friction (0.4), it appears as though both boxes begin to move at the same angle, being 21.8.


This is simply very counterintuitive to me, and I want to make sure I'm not misunderstanding how the formulae work. Am I right that both boxes begin to move at the same angle?
 
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That's correct and perfectly reasonable- the downward force on each crate is proportional to its weight and the static friction is proportional to its weight. The two proportions cancel.
 
Yes you are correct. The angle at which an object begins to slide is, as you discovered, independent of its mass, and depends only on the value of the static friction coefficient (u = tan theta)
 
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