First slide

Application of Newtons laws

Question

All surfaces are smooth. Find acceleration of triangular in m/s². $(Take g = 9 m / s^{2})$

Moderate

Solution

$\begin{array}{l} N \sin θ = 2 m a_{2} . . . . . . (i) \\ m g - N \cos θ = m a_{1} . . . . . . . (i i) \end{array}$
Also, from constrained relation,
$\begin{array}{l} a_{2} \sin θ = a_{1} \cos θ \\ ∴ a_{1} = a_{2} \tan θ . . . . . . . (i i i) \end{array}$
From Eqs. (i), (ii) and (iii), $m g - N \cos θ = m a_{1}$
$\begin{array}{l} or m g - \frac{2 m a_{2}}{\sin θ} \cos θ = m a_{2} \\ or g - 2 a_{2} \cot θ = a_{2} \tan θ \\ or g = (2 \cot θ + \tan θ) a_{2} \\ ∴ a_{2} = \frac{g}{2 \cot θ + \tan θ} = \frac{9}{3} = 3 m / s^{2} \end{array}$

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