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How to determine a formula for the acceleration of the system of the two blocks?
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How to determine a formula for the acceleration of the system of the two blocks?
A block (mass m1) lying on a frictionless inclined plane is connected to a mass m2 by a massless cord passing over a pulley, as shown in the figure. This is the additional part of the problem and the formula has to be in terms of m1, m2, θ and g.
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Forces acting on Mass 1:
\(T_1=m_1\cdot(a)+m_1\cdot (g)\cdot (\sin \theta )\)
Forces acting on Mass 2:
\(T_2=m_2\cdot(g)-m_2\cdot(a)\)
Set T1 = T2:
\(m_1\cdot (a)+m_1\cdot (g)\cdot (\sin \theta )=m_2\cdot (g)-m_2\cdot (a)\)
Solve for (a) by bring all terms containing 'a' to one side of your choosing:
\(m_1(a)+m_2\left(a\right)=-m_1(g)(\sin \theta )+m_2(g)\)
Factor out the 'a' term on the left-side:
\(a\left(m_1+m_2\right)=-m_1(g)(\sin \theta )+m_2(g)\)
Divide both sides by m1 + m2:
\(a=\frac{-m_1(g)(\sin \theta )+m_2(g)}{m_1+m_2}\)
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