How to find the acceleration of a car ascending in an incline when a sphere makes an angle in a quarter of a circle cavity?

Jun 2017
337
6
Lima, Peru
The problem is as follows:

The figure from below shows a car going up in an incline. The car has a circular cavity on it where there is a small sphere over it. Assume the circular surface has negligible friction. Given these conditions find the acceleration in meters per second square which the wagon must have so that the ball takes the position as shown in the diagram.



The alternatives given are as follows:

$\begin{array}{ll}
1.&9.80\,\frac{m}{s^2}\\
2.&8.33\,\frac{m}{s^2}\\
3.&6.25\,\frac{m}{s^2}\\
4.&5.66\,\frac{m}{s^2}\\
5.&4.57\,\frac{m}{s^2}\\
\end{array}$

In this problem I'm not sure how to proceed. But my instinct tells me that the acceleration of ascention must be equal to the centripetal acceleration of the ball. But I'm confused exactly at how show I make FBD or something similar to see how forces are acting on the body, therefore a draw or sketch would be appreciated in order to spot exactly the justication of the following calculations.

If I were to ignore the thing that the wagon is on an incline, the bob would have:

$mgcos 37^{\circ}=\frac{mv^2}{R}$

In this case the masses cancel, and the answer would be just $g\cos 37^{\circ}$. But this doesn't convince me much. Can someone help me here?.
 

skeeter

Math Team
Jul 2011
3,266
1,766
Texas
Reference the diagram ...

$\vec{N} + \vec{W} = \color{red}\vec{F_{net}}$

I get choice (5).

incline_mass_qtrCircle.jpg
 
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