The math help thread

I'd assume y = kx where k = -h/b is the formula for the triangle then. If that's the case, what length is the triangle? Is that given, or is that a variable? (I'm very confused.)

Man you must live in a different mathematical universe or something o.O

Triangle is b wide and h high. Rise over run. Simple as that. Remember that the triangle is on the left side of the y-axis.

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.

Freebody diagrams are fun! Hooray!

Top:
In order to do this problem correctly, we'd need a few more assumptions. For both of our sake, I'm assuming the system is at rest. This means that the following equations are true:

ΣForce = 0
ΣTorque = 0

I'm also going to assume that the mass can swing around the pin, or else the pole/wall comes into play, making the problem even more complicated.

Next, we find out all the forces involved. Red arrows are total forces, and green arrows are component (x,y) forces.

 Free body diagram

Since ΣF = 0, ΣT = 0, and the component forces in one direction have no bearing on forces in another direction, set up equations for the system and solve. For the last equation, we're taking the torque around the pin.

Code:

Fp = pin force
Fr = rope force
Fm = mass force = 10kg * 9.8m/sec^2

98 = Fr*sin(45) + Fp*sin(θ)
Fr*cos(45) = Fp*cos(θ)
0 = 98*1 + Fr*sin(45)*2