Moments

ssj

I cant seem to work it out correctly the force is L/2 away from the pivot and in order to work out the tension I must do something must I make T perpendicular ?

Doc Al

You treat the tension in problem 2 exactly as you did in problem 1.

Doc Al

You might want to study these examples: Torque Equilibrium Examples

ssj

Right to in problem 1 we basically made it perpendicular correct ? So for now lets call the lenght L meaning that 200*L=200*T*sin30, sin30 because that will give use the hypotenues which is T but the problem with the formula is that it gives the same answer as we got in question 1 meaning we must divide sin30 on each side meaning 200*L/sin30= 400 and once we find out the L we will get an new answer perhaps.

Doc Al

Yes.
If you're talking about problem 1, that should be:
200*L = L*T*sin30

Using the corrected equation, we get: T = 200/sin30 = 400 N. The L drops out and has no bearing on the answer for tension. If the beam were twice as long, you'd still get the same tension.

If you are talking about problem 2, the left side of the equation is different. The distance is not L, but L/2. The right side remains the same, since the cable has not moved and the angle is the same.

Rewrite the equation for problem 2 and solve for the tension. Again, the length of the beam (L) will drop out.

ssj

Yes I think i understand 200*L/2=L*T*sin30
Which becomes 200/sin30/2
400/2=T
200=T

Doc Al

Good! In the second problem it takes just half the tension to support the beam.

ssj

What about this question


My guess is something like 400*L/4=L*T*sin30

Doc Al

The right side is correct, but the left is not. Don't guess! You have two forces producing clockwise torques--add up the torque from each. You should know the torque from each one, since they are the same forces as appeared earlier.

ssj

So the torque from question 1 was 400N and question 2 was 200N meaning we have
600*L/2=L*T*sin30.

Doc Al

Those were the tensions, not the torques. The clockwise torque from problem 1 was 200*L; from problem 2 it was 200*L/2.

ssj

Right this makes it 400*L/3=L*T*Sin30

Doc Al

No:
200*L + 200*L/2 = 200*(3L/2)

ssj

How did you get "3L/2" on the right hand side and why isit L/2 on the left side ? Furthure more once I calcualted this euqation L=200 where do I go from here?

Doc Al

This is not the equilibrium equation, this is just the sum of the clockwise torques (see post #43): 200*L + 200*(L/2) = 200*(3L/2) = 300*L

Now set this sum of clockwise torques equal to the counter-clockwise torque due to the tension to the get the equilibrium equation:
300*L = L*T*sin30

Now you can solve for the tension in problem 3.

ssj

For the sum of the clockwise torques I understand that 200*L+200(L/2) but I don't understand 200*(3L/2) where did the "3L" come from ?

Doc Al

L + L/2 = 3L/2
You can also write that as: (3/2)*L

You can also do this:
200*L + 200*(L/2) = 200*L + 100*L = 300*L

Please convince yourself that these are equivalent.