Question

MAJOR POINTS! Solve the system of equations to find =" a_{2} " alt=" a_{2} " align="absmiddle" class="latex-formula">

Answer 1

You are dealing with pulleys?

can be done with addition of the two equations to eliminate T.

$(2^{*}) \quad {} -m_1 g \cos \theta + T = m_1 a _2$
+
$(4^{*}) \quad 3m_1 g - T = 3m_1 a_2$
=

$(-m_1 g \cos\theta + 3m_1 g) + (T - T) = m_1 a _2 + 3m_1 a_2 \implies \\ \\ (-m_1 g \cos\theta + 3m_1 g) = 4m_1 a_2 \implies \\ \\ m_1(- g \cos\theta + 3g)= 4m_1 a_2$

we can cancel m₁ by dividing both sides by it, assuming mass is not zero


$(- g \cos\theta + 3g)= 4a_2 \implies \\ \\ a_2 = \dfrac{- g \cos\theta + 3g}{4} \\ \\ a_2 = \dfrac{- 9.80 \cos 60 + 3(9.80)}{4} \\ \\ a_2 = 6.125 \text{m/s}^2$

a₂ = 6.125 m/s² ( do significant digits if you need to)