Inclined plane pulley problem -- lab report help please

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SUMMARY

The discussion centers on the inclined plane pulley problem, specifically the equation for acceleration: a = (m2g - m1g sin(ø) - m1g cos(ø)u) / (m1 + m2). Participants emphasize the importance of parentheses in mathematical expressions and clarify that linearization in this context does not yield a linear equation unless specific approximations are applied. The conversation also highlights the need for a visual diagram to better understand the experimental setup and the implications of small angle approximations.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with trigonometric functions and their applications
  • Knowledge of linearization techniques in calculus
  • Ability to interpret and create scientific diagrams
NEXT STEPS
  • Study the derivation of the inclined plane pulley acceleration equation
  • Learn about small angle approximations in physics
  • Explore the concept of linearization in calculus with practical examples
  • Review methods for creating effective scientific diagrams for experiments
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Students in physics, educators preparing lab reports, and anyone involved in experimental mechanics will benefit from this discussion.

Jimmyjonny12
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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
 
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Welcome to the PF. :smile:

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
 
Jimmyjonny12 said:
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.
 
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.
 

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