Solve Torque Question: Will Free Point B Go Up?

[toqp]

Homework Statement

http://img21.imageshack.us/img21/7103/fig1jpg.png

The rods in the system are rigid and massless. The only mass in the system is that of the weight (mass m).

The system as a whole is pivoted at a point A. The lower rod is pivoted at a point C.

If the system is set correctly, will the free point B go up?

The Attempt at a Solution

Of course there's first the torque T of the lower rod. It is supposed to be in balance so the sum must be zero. If the gravitational force acting on the mass is mg, then there is some force F acting on the point where the upper and lower rods meet.

$$\sum T = mgr_b - Fr_c = 0 \Rightarrow F=mg\frac{r_b}{r_c}$$

(It seems my latex code is not working, so..)

T = mgr_b - Fr_c = 0 --> F=mg (r_{b / rc})

When considering the whole system, we can think of the mass m as acting at the point C, so that it tries to rotate the whole system down.

$$T_{down}=mgr_a$$

T_down=mgr_a

On the other hand, if the lower rod is kept stationary, the there must be a force equal to F acting at the point r_a + r_c.

$$T_{up}=F(r_a + r_c)$$

T_up=F(r_a+r_c)

So yes... the point B can move upwards. But this seems so counter-intuitive to me. I surely have missed something or done something wrong.

 

[toqp]

Edit:

Of course... I've completely forgotten translational conditions. The pivotal point C is not translationally at rest.

 

[nlightner]

As a scientist, my response would be that the analysis provided in the attempt at a solution is correct. According to the equation T = mgrb - Frc = 0, if the force F is greater than the weight of the mass (mg), then the point B will move upwards. This may seem counter-intuitive, but it is a result of the fact that the force F is acting at a greater distance from the pivot point than the weight of the mass, thus creating a greater torque. The key factor to consider here is that the system is in equilibrium, meaning that the sum of all torques must be equal to zero. Therefore, the force F must be strong enough to counteract the torque created by the weight of the mass in order for the system to remain in equilibrium.