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The problem is as follows:

The figure from below shows a wagon going down along an incline with a tilt angle $\omega$. Assume the wire holding the bob is paralell to the surface which supports the incline. Given this condition, find the magnitude of the acceleration that the wagon has when it is going down the incline.

Sketch of the problem

The alternatives are as follows:

$\begin{array}{ll} 1.&g\sin\omega\\ 2.&g\cos\omega\\ 3.&g\tan\omega\\ 4.&g\sec\omega\\ 5.&g\csc\omega\\ \end{array}$

In this problem I'm totally lost at. But my guess it is that the centripetal acceleration experienced by the bob is the same as the wagon when it is going down.

But the problem arises from the fact that I'm unable to establish an equation which can relate this with the incline. Can someone help me with this?.

In these kind of situations typically what we have to use is:

$T-mg\cot\omega=m\frac{v^2}{R}$

But I'm not given the radius. And the function I obtained it from the angle that the wire is with the weight to be $90^{\circ}$. But yet I'm still stuck on here. Can somebody help me?.

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1 Answer 1

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Establish the equilibrium equations below for the bob

$$T\sin w = mg\cos w,\>\>\>\>\> T\cos w + mg \sin w = ma$$

Eliminate $T$ to obtain

$$a = g\>\csc w$$

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  • $\begingroup$ Can you please add a FBD to see how did you get those equations?. I'm confused exactly how to see where the tension is pulling the bob with respect of the incline. Can you help me with that part?. $\endgroup$ Feb 2, 2020 at 19:17

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