How to find the magnitude of the acceleration of descend from a wagon in an incline given a bob is tied to its roof?

Jun 2017
337
6
Lima, Peru
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.



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?.
 

skeeter

Math Team
Jul 2011
3,266
1,766
Texas
let $m$ be the mass of the bob.

sketch the two forces acting on the bob, the resultant of which is $F_{net} = ma$.

$ma \sin{\omega} = mg$
 
Jun 2017
337
6
Lima, Peru
let $m$ be the mass of the bob.

sketch the two forces acting on the bob, the resultant of which is $F_{net} = ma$.

$ma \sin{\omega} = mg$
Can you please help me drawing the FBD for this case? I can't see exactly where are the forces acting on the body. But I suspect that the acceleration is the resultant of the tension in the wire plus the weight of the bob. Am I right with this?. Im still stuck here.
 

skeeter

Math Team
Jul 2011
3,266
1,766
Texas
$\vec{F_{net}} = m\vec{a} = \vec{T} + \vec{W}$

net force has the same direction as the wagon's acceleration