The question states:

What is the mass of the brass weight hanging from the end of the string if the system is at equilibrium?

A. 2.3 kg

B. 3.0 kg

C. 4.6 kg

D. 6.0 kg

I believe I understand this concept, that equilibrium means that the torque of the beam+m2 is supposed to be equal to the torque of the string at the hinge.

What I do not understand was how they solved for the problem. So torque is acting on three things: the beam, the mass 2, and the string. They said the torque of the beam was equal to 2 (where did they get this value from? 2 is the mass of the beam. I thought we were solving for torque, which is

**t=r**

**L****sinθ**, what does mass have to do with this equation?) * 10 (I suppose this is 10m/s^2 of to acceleration due to gravity) * 0.25 (the distance of the beam from the hinge to the string attachment point). Then they set the torque of the beam equal to the torque of mass 2, which is equal to 1 (again, the mass of m2, but again... why is mass included? What does mass have to do with torque?) * 10 (acceleration due to gravity) * 0.5 (the length of the entire beam). What is confusing is that it seems like to find the torque of the beam and the torque of m2, I use the mass, the acceleration due to gravity and length of it's position on the beam. So essentially to find these two torques, beam and m2, I use the equation t= mgL? Why am I using the mass to find the torque? This is where I am confused.

Okay, so going further, both the torque of the beam and the torque of the mass 2 equal 5Nm. So the torque of the string must equal 10Nm to offset the torque(s) of the beam + m2. So we have the torque of the string,

**t= 10Nm**, which is set equal to

**r**

**F****sinθ**. I see that you need the force to solve for the mass. In a situation similar to randomly switching to mass, we now switch to force. How do you intuitively know when to switch from

**in the equation? This is not the time for a "you get it or you don't" scenario; I'm tired of getting problems like these wrong. I literally need to know how do you know when to modify the equation and when you know that you need to use Force instead of Length at this time in the process of solving for this equation?**

*m to f to l*Sincerely,

-Ariel Morrow