Inclined plane pulley problem -- lab report help please

[Jimmyjonny12]

Homework Statement

Hi I have a lab report where I have to linearise the equation below so that it becomes y=mx+c where y= acceleration(a) and x= angle of inclination(sinø) this is all I have gotten to so far

Relevant Equations

a=m2g-m1gsinø-m1gcosøu/m1+m2

u=friction coefficient

a=m2g-m1gsinø-m1gcosøu/m1+m2

 

[berkeman]

Welcome to the PF.

Is there a diagram that goes with this lab experiment/report? It's hard to visualize the setup from your explanation. You can use the "Attach files" button below the Edit window to upload a PDF or JPEG image of the problem. Thanks

 

[haruspex]

a=m2g-m1gsinø-m1gcosøu/m1+m2

I believe you mean $a=\frac{m_2g-m_1g\sin(ø)-m_1g\cos(ø)u}{m_1+m_2}$. Parentheses matter!
Not sure what you mean by linearising in this context. If you substitute y for a, x for sin(ø) and √(1-x²) for cos it will not yield a linear equation. Applying a small angle approximation would not make it linear unless you take the cos to approximate 1.

 

[lightlightsup]

Linearizing an equation at a particular x-value(a): L(a)=f(x)+f'(x)(x-a).
See: https://en.wikipedia.org/wiki/Linearization
You're just getting the equation of the line tangent to the curve at that point.
I don't know if that is what your lab is asking you to do.