Question

MAJOR POINTS! Solve the system of equations to find
`a_(2)`

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 = (- g \cos\theta + 3g)/(4) \\ \\ a_2 = (- 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)