Empty Box with Plumb Bob Sliding Down a Plane

[Karina]

Homework Statement

You hang a plumb bob inside an empty box. The empty box slides down a friction-less inclined plane. The inclined plane makes an angle of 30 degrees with the horizontal. What is the angle the plumb bob makes with the vertical during the slide?

Homework Equations

g pulled down on the string at 9.81 m/s^2... and the Tension = should be the same in the opposite direction

The Attempt at a Solution

I know that the box is accelerating down the slide and the string continues to exert an upward force on the plumb bob to balance the gravity acting on it. The plumb bob should hang an angle towards the back of the box. I tried to draw it out but I am not even sure if I have it right so far.

 

[Satvik Pandey]

Hi Karina. Welcome to PF.:)

Can you draw the free body diagrams of box and bob?
Do you know have knowledge about pseudo force?

 

[Karina]

Not sure if this will suffice? Is that correct? We haven't gone over that in class yet but I am aware that it's a fake force, like something we make up. Is that what I was thinking earlier in the explanation, a pseudo force?

 

[Satvik Pandey]

Not sure if this will suffice? Is that correct? We haven't gone over that in class yet but I am aware that it's a fake force, like something we make up. Is that what I was thinking earlier in the explanation, a pseudo force?

Yes pseudo force is a fake force.

Figure 1 is the FBD of the box and Figure 2 is the FBD of the bob.
Here I am considering a reference frame which is moving with the box. As it is a non-inertial frame of reference so we have to consider a pseudo force. Can you find the magnitude of pseudo force acting on the bob?

 

[Karina]

Isn't the pseudo force = m2g+T?

 

[Satvik Pandey]

Isn't the pseudo force = m2g+T?

No, why?
You have to find the magnitude of pseudo force in terms of $m_{2}$,$g$ and $\theta$.

 

[Satvik Pandey]

Please visit this link to find more about pseudo forces.
http://en.wikipedia.org/wiki/Fictitious_force.

There are also many video lectures on youtube about pseudo forces. You can also refer to them.

 

[Karina]

Pseudo force = m2gsintheta

 

[haruspex]

Pseudo force = m2gsintheta

That's the magnitude, but you should also state the direction. Now combine it in an equation with the other forces on m2.

 

[Satvik Pandey]

Pseudo force = m2gsintheta

Yes that's correct.
I have also specified the direction of this pseudo force in #Post 4.

In this figure I have drawn the FBD of that bob. Consider force 'P' in the figure as pseudo force.
In figure I have also specified the the axis. Just find the components of forces along the X and Y axis and construct equation using second law.
For that you have to find the value of angle which I have mentioned. Can you find it?

 

[BvU]

Don't intend to get into a fight about pseudo forces (I avoid them as much as I can).
But let me at least emphasize there's no need for them in this exercise:

The bob hangs from a rope, so it "feels" the tension of the rope, and the Earth is pulling on it straight down.
That's all the forces it "feels". If it's to accelerate down the slide at the same rate ($\ g\sin\theta\$) as the box (i.e. not swing around like puppet on a string), the net vector sum has to be $mg\sin\theta\;$. In other words, the string has to compensate ( $mg\;$ straight down ) minus ( $mg\sin\theta\;$ downwards along the slope).

Much simpler...