The math help thread

I don't really understand how to do these two Physics problems:

Top: Calculate the force of the pin joint and the tension in the rope.


Bottom: Determine the mass needed to balance the beam in the figure.

 Spoiler

For the bottom one, I think the force*distance on both sides needs to be equal. Since we're talking gravity, that's proportional to mass*distance.
Since it's a meterstick, the distance between each of those dots is 10cm (though it actually doesn't matter). The 40cm of meterstick on either side of the balance point cancel out, leaving the 20cm on the right, which is 20% of the meterstick.
That part of the meterstick weighs 10g and its midpoint is 50cm to the right of the balance point, so its mass*distance is 500g*cm.
The mass you're trying to find is 20cm left of the balance point, so it's 500g*cm/20cm = 25g

Disclaimer: I haven't taken any Physics beyond 8th grade "Physical Science."