Finding the Angle When the Crate Begins to Slip

[Graydon Hope]

Homework Statement

A crate is placed on an adjustable, inclined board. The coefficient of static friction between the crate and the board is 0.29. A) Calculate the angle at which the crate just begins to slip.

Homework Equations

Sum of Forces=M*A

The Attempt at a Solution

In my problem: Why is g cancelled? and why is 0.29 added to tan^-1
These are highlighted areas

 

[phinds]

Your picture is so tiny it is not readable

 

[Graydon Hope]

Hmm weird.. I can see it clearly even from my phone. Its my first post maybe I messed something up.

 

[Graydon Hope]

Your picture is so tiny it is not readable

Weird.. I can see it from my phone clearly. Maybe I did something wrong

 

[scottdave]

so it looks like you have in the one section: = 0 < g*(sinθ - μ*cosθ). Just multiply both sides by 1/g and you have 0/g < (g/g)*(sinθ - μ*cosθ). 0/g is 0, and g/g is 1.
For the last part, they get it down to μ < tanθ, then plug in μ=0.29 which is given in the problem statement. Take inverse tangent of both sides to find θ.

 

[TomHart]

When I was young, I had excellent near vision. Now . . . not so much. However, even when I downloaded the photo and zoomed in, I can still see well enough to realize there is a shortage of pixels; it is still very difficult to read. "And things that are too hard just aren't worth doing," said someone.

Welcome to Physics Forums.

 

[haruspex]

even when I downloaded the photo and zoomed in, I can still see well enough to realize there is a shortage of pixels; it is still very difficult to read.

Strange.. if I click on the link it takes me to https://www.physicsforums.com/attachments/img_20170525_213308-jpg.204257/, an image that is quite readable even with my so-so vision. (But it is so misaligned to the frame that the top right corner is missing.)
Anyway, scottdave has posted the answers to the OP questions.