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A steel washer is suspended inside an empty shipping crate from a light string attached to the top of the crate. The crate slides down a long ramp that is inclined at an angle of 36^\circ above the horizontal. The crate has mass 156 {\rm kg}. You are sitting inside the crate (with a flashlight); your mass is 64 {\rm kg}. As the crate is sliding down the ramp, you find the washer is at rest with respect to the crate when the string makes an angle of 66^\circ with the top of the crate.

So far, I've just figured out:

y: n=m

_{crate+person}gcos(theta)

x: f

_{k}-m

_{crate+person}gsin(theta)=ma

u(m

_{crate+person}gcos(theta))-m

_{crate+person}gsin(theta)=ma

u=[a+gsin(theta)]/(gcos(theta))

so using that I got g=9.8m/s^2, theta=36, m

_{crate+person}=220kg, but I don't know what a is...

my question is... Do we have to use the additional information (the washer) to find a? if so, how would we solve for a?