Which box will start to slide first?

[Kelsob]

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?

 

[HallsofIvy]

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.

 

[PhanthomJay]

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)