How can I find the length of this pole?

In summary, the problem involves determining the length of a pole supported by a cable and acted upon by a force of magnitude 70 lb at point B. The given information also includes the moment of this force about the x-axis. The solution involves using the equations for torque or moment of force and finding the vectors for the force and the point of application. The attempt at a solution involves finding the vector for the force and the point of application and using the determinant to calculate the torque, but the resulting units do not measure length.
  • #1
GaussianSurface

Homework Statement


A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght.
I'LL ATTACH AN IMAGE SO YOU CAN SEE IT.

Homework Equations


τ= torque or moment of force
τ= r X F
Tτ= T1+T2
Tτ=(r1 + r2) x F

The Attempt at a Solution


I don't know how to compute the lenght, I was thinking about it maybe was related with the torque or moment of force (let me know if this is true).
What I tried to do was this:
r1= 4i + 6k
e= 4i+6k
e=√4^2+6^2
e=√52
e=4/√52 + 6/√52

F= 70(4/√52 + 6/√52) = 38.82i+58.24k
and by performing the determinant

τ= -0.04 lb/ft
So far I should've got the T1 and now I'd do the same but this time with other vectors ⇒ 4i-6k

I don't think it's correct since I got a result on differents units that don't measure the lenght. PLEASE TRY TO TELL WHAT I'M WRONG AND WHAT I'M RIGHT.
 

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  • #2
GaussianSurface said:
r1= 4i + 6k
How are you defining r1? That does not look like a useful vector.
The force is directed along BA. Can you write down that vector?
The point of application of the force is B, so you also need the vector OB. Can you write that down?
 

1. How do I measure the length of the pole?

To measure the length of the pole, you can use a measuring tape or ruler. Place one end of the measuring tool at the base of the pole and extend it until you reach the top. Make sure the measuring tool is straight and parallel to the pole for an accurate measurement.

2. Can I estimate the length of the pole?

Yes, you can estimate the length of the pole by using a familiar object as a reference. For example, if the pole is about the same height as a door, you can use the height of the door to estimate the length of the pole.

3. What if the pole is not completely straight?

If the pole is not completely straight, you can still measure its length by using a flexible measuring tape. Wrap the measuring tape around the pole, following its curvature, and measure the distance from one end to the other. Alternatively, you can use a string to measure the length and then measure the string with a ruler.

4. How accurate will my measurement be?

The accuracy of your measurement will depend on the precision of your measuring tool and your technique. It is important to ensure that the measuring tool is straight and parallel to the pole for an accurate measurement. If you are using an object as a reference for estimation, the accuracy may vary.

5. Can I use a different unit of measurement for the pole?

Yes, you can use any unit of measurement as long as it is consistent. For example, if you measure the pole in feet, make sure all your measurements are in feet. This will ensure accurate comparisons and calculations.

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