Washer Hanging from Box Moving Down a Ramp

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A steel washer is suspended inside a shipping crate sliding down a 37° ramp, with the crate's mass at 180 kg and an occupant's mass at 55 kg. The washer remains at rest relative to the crate, making a 68° angle with the top of the crate. The discussion focuses on deriving the equations for the forces acting on the washer to find the coefficient of kinetic friction between the ramp and the crate. The equations involve analyzing the tension in the string and the gravitational forces acting on the washer. Clarification is sought on the origin of the force equations for the washer, indicating a need for deeper understanding of the physics involved.
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Homework Statement


A steel washer is suspended inside an empty shipping crate from a light string attached to th top of the crate. The crate slides down a long ramp that is inclined at an angle of 37° above the horizontal. The crate has mass 180kg. You are sitting inside (with a flashlight); your mass is 55kg. As the crate is sliding down the ramp, you find the washer is at rest with respect to the crate hen the string makes an angle of 68° with the top of the crate. What is the oefficient of kinetic friction between the ramp and the crate?


Homework Equations


ƩF=ma
fk=μn


The Attempt at a Solution


Let mc = mass of crate
and my = mass of you
and m = mass of washer
ƩFcrate system = (mc + my)a = (mc + my)gsin(37) - μ(mc + my)cos(37)

Canceling out the combined mass and solving for μ gives:

μ = [gsin(37) - a]/[gcos(37)]

Apparently...
Let T = tension in string
ƩFy-washer = ma1 = Tsin(22) -mgsin(37)
and
ƩFx-washer = ma2 = Tcos(22) -mgcos(37)

And a2 = 0 allowing for these two equations to be rearranged and then divided by each other giving...
tan(22) = [gsin(37) - a]/[gcos(37)]

My actual question:

Where are the ƩFwasher equations coming from? I have the attached picture to help, but I still don't understand.
 

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Where are the ƩFwasher equations coming from? I have the attached picture to help, but I still don't understand.
Free body diagram for the washer.
So you didn't derive the equations yourself then?

You can also look at it from the POV of you - if the crate were stationary on the slope, what angle would the washer make to the ceiling?
 

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