# Calculate the tension in the string

by ssj
Tags: moments
Mentor
P: 41,579
 Quote by ssj So this would make it 300*L=L/2*T*Sin30 ?
You now have the correct distance on the right-hand side (L/2), but what happened to the angle?
P: 36
 Quote by Doc Al You now have the correct distance on the right-hand side (L/2), but what happened to the angle?
Sorry about that I meant Sin50.
Mentor
P: 41,579
 Quote by ssj Sorry about that I meant Sin50.
Good! (I thought so.) Now you can solve for the tension--once again, the actual value of L doesn't matter.
P: 36
 Quote by Doc Al Good! (I thought so.)
Right so the equation now becomes 300*L=L/2*T*Sin50.
Mentor
P: 41,579
 Quote by ssj Right so the equation now becomes 300*L=L/2*T*Sin50.
Yep.
P: 36
 Quote by Doc Al Yep.
So if I replace L with 2 I get T=600/sin50 meaning T=783.

Now im stuck with the following question .

I cant seem to understand how to work the answer out.
Mentor
P: 41,579
 Quote by ssj So if I replace L with 2 I get T=600/sin50 meaning T=783.
Correct. But realize you don't have to "replace" L with any number--the L just drops out:
300*L=L/2*T*Sin50 becomes 300=1/2*T*Sin50 if you cancel the L on both sides. (Which means dividing both sides by L.)

 Now im stuck with the following question ...
Another equilibrium problem. What are the conditions for equilibrium? Forces must add to zero and torques about any point must add to zero. Label the vertical support forces (at each end of the bridge) F1 & F2. Hint: A good point to use as a pivot is either end of the bridge.
P: 36
 Quote by Doc Al Another equilibrium problem. What are the conditions for equilibrium? Forces must add to zero and torques about any point must add to zero. Label the vertical support forces (at each end of the bridge) F1 & F2. Hint: A good point to use as a pivot is either end of the bridge.
Alright so if I lable the force between 4kN and 10kN F1 and from 10kN to 8kN F2 and place an pivot at the left hand side of the bridge would this be correct and what would the equation be for the clockwise rotation= counter clockwise rotation ?

As seen below
Mentor
P: 41,579
 Quote by ssj Alright so if I lable the force between 4kN and 10kN F1 and from 10kN to 8kN F2 and place an pivot at the left hand side of the bridge would this be correct and what would the equation be for the clockwise rotation= counter clockwise rotation ?
No. F1 is the upward force of the support on the left end of the bridge, F2 is the upward force on the right end of the bridge.

If you pick the left side of the bridge as your pivot, you will have the three axial loads producing the clockwise torques and the force F2 producing the counter-clockwise torques. Find those torques just like in all the previous problems.
 P: 36 Would it be *F1 14kN*10.5M=8kN*5.25M*F2 ? am I correct ?
Mentor
P: 41,579
 Quote by ssj Would it be *F1 14kN*10.5M=8kN*5.25M*F2 ? am I correct ?
No. There are three forces (each at a different distance from the pivot) that create clockwise torques. And the force F2, which creates the counter-clockwise torque, is how far from the pivot?

I encourage you to study the examples discussed on the webpage I linked in post #37.
P: 36
 Quote by Doc Al No. There are three forces (each at a different distance from the pivot) that create clockwise torques. And the force F2, which creates the counter-clockwise torque, is how far from the pivot? I encourage you to study the examples discussed on the webpage I linked in post #37.
Alright so is this correct ?

Meaning that ths distance from the pivot is 5.25M+5.25M?
 Mentor P: 41,579 No, the distance of F2 from the left pivot point is: 7m + 3.5m + 5.25m + 5.25m = 21m. (You didn't even have to do that addition: the problem states that the bridge supports are 21m apart.)
P: 36
 Quote by Doc Al No, the distance of F2 from the left pivot point is: 7m + 3.5m + 5.25m + 5.25m = 21m. (You didn't even have to do that addition: the problem states that the bridge supports are 21m apart.)
I think the total Clockwise force F1 would be equal to 22kN*21m=462 correct but what would the counter clockwise force be then?

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