Forces acting on a support point after the system is released

[IgorT75]

Summary:: What is the force N which acts on a support point at the moment just after system is released?

[Thread moved from the technical forums, so no Homework Template is shown]

A light bar with m1 and m2 masses (m1≠m2) at the ends placed on the support point (in the middle of the bar).
Initially it is held in this position (by hands let's say). Then it's released.
What is the force N which acts on a support point at the moment just after system is released?

 

[etotheipi]

It is customary that you show an attempt; however I will offer three bits of information that might be useful.

1. The net force on a body equals the total mass of the body multiplied by the acceleration of it's centre of mass. See Euler's equations of motion.

2. The net torque on a rigid body about a chosen origin equals the rate of change of its angular momentum about that origin (or here better expressed with moment of inertia & angular acceleration...?)

3. The acceleration of a point on the rigid body w.r.t. point on the rigid body that is fixed in the lab frame is $\vec{a} = \vec{\alpha} \times \vec{r} + \vec{\omega} \times (\vec{\omega} \times \vec{r})$. But what is the initial $\vec{\omega}$?

A few things to think about!

 

[IgorT75]

@etotheipi : I really was thinking about this problem, and all your points are valid.
But I don't see a motion in this problem - better say I don't see how to introduce it.
Neither do I understand how to introduce acceleration.
Any suggestion will help.

 

[etotheipi]

OK. First of all, let us suppose WLOG that $m_1 > m_2$. Hopefully you can see that this will cause the configuration to go into rotation.

Now, let your system consist of the rod and the two masses. This system is acted upon by two gravitational forces, $m_1 \vec{g}$ and $m_2 \vec{g}$, as well as a normal contact force $\vec{N}$ from the hinge. The vector sum of these forces is then $(m_1 + m_2)\vec{a}_{cm}$.

Second of all, where is the centre of mass w.r.t. the hinge? And finally, what is the angular acceleration of the configuration (apply $\tau = I\alpha$ about the hinge!).

Try and write down some equations, and go from there!

 

[jbriggs444]

Let me try to back up a step explain how one might attack the problem and thereby decide to do what @etotheipi is suggesting.

You have an unknown force acting at the support point. You have a problem involving rotation. This is a big clue that you should choose an axis of rotation at the support point. Then do a torque balance and see if you can solve for something. Net torque, Angular acceleration, Whatever you can solve for.

Rule of thumb: put your axis of rotation where the unknown force acts. That way the unknown force will not produce any torque.

The hope is that once you solve for what you can solve for, the result will help you calculate what you are really after.

 

[IgorT75]

@jbriggs444 & @etotheipi : Thanks for actually not giving me solution because I really want to solve it myself.
Will try your suggestions little later and let you know.
Thanks!

 

[IgorT75]

Figured it out. Use of center mass was an idea which helped me a lot.
$$(m_2−m_1)gr=Iε=(m_2+m_1)r^2\varepsilon$$Force $F$ and accelaration $a_c=\varepsilon x$ at center of mass:
$$F=Ma_c=(m_1+m_2)a_c$$Forces acting:$$F=(m_1+m_2)g−N$$Assume $m_2>m_1$ and center of mass is at distance x from support point. Then:
$$x=\frac {l(m_2−m_1)} {2(m_1+m_2)}$$Finally:$$N=(m1+m2)∗g−F=...=\frac {4m_1m_2g} {m_1+m_2}$$Thanks to all!