- #1
youngstudent16
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Homework Statement
Below are four equations, with the known quantities listed. Solve these equations to obtain an expression for ##T## in terms of known quantities only. Do the same to obtain an expression for ##a##
##T-f=m_1a\hspace{5mm}N-m_1g\cos\theta=0##
##m_2g-T=m_2a \hspace{5mm} f=\mu N##
##m_1,m_2,\mu,g,\theta## Are known quantities
Unknown quantities are ##T,a,N,f##
Homework Equations
Knowing how to solve system of equations
The Attempt at a Solution
My attempt and I'm wondering if I can solve this easier with a matrix.(or if this was correct I have not done these that often)
##N=m_1g\cos\theta##
##f=\mu m_1g\cos\theta##
Now I have two equations and two unknowns
##T-\mu m_1g\cos\theta=m_1a##
##m_2g-T=m_2a##
##T=m_1a+\mu m_1g\cos\theta##
##m_2g-m_1a+\mu m_1g\cos\theta=m_2a##
##m_1\left(-a+\mu g\cos\theta\right)=m_2(a-g)##
##\frac{m_1}{m_2}+g=\frac{a}{\left(-a+\mu g\cos\theta\right)}##
##\frac{m_1}{m_2}+g+1=\frac{a}{\left(\mu g\cos\theta\right)}##
##\left(\mu g\cos\theta\right)\left(\frac{m_1}{m_2}+g+1\right)=a##Now just plug ##a## back in for the first. Is that correct and is there an easier way to do this with a matrix?
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