## Related questions with answers

Question

Collar A is free to slide with negligible friction on the circular guide mounted in the vertical frame. Determine the angle $\theta$ assumed by the collar if the frame is given a constant horizontal acceleration a to the right.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2The force balance of collar in $x$-component is,

$\begin{align*} N \sin \theta &= ma \tag{1} \end{align*}$

The force balance of collar in $y$-component is,

$\begin{align*} N \cos \theta &= mg \tag{2} \end{align*}$

Divide ($1$) by ($2$),

$\begin{align*} \dfrac{N \sin \theta}{N \cos \theta} &= \dfrac{ma}{mg} \\ \tan \theta &= \dfrac{a}{g} \\ \implies \theta &= \boxed{\tan^{-1} \left( \dfrac{a}{g} \right)} \end{align*}$

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