Wrecking ball torque question

1. Apr 27, 2017

1. The problem statement, all variables and given/known data
At one point during its swing, a wrecking ball exerts a tension force of 9800 N on its cable, which makes an angle of 30 degrees with the horizontal. The crane's 9 m long boom is at an angle of 55 degrees with the horizontal. What is the torque exerted by the wrecking ball on the crane about an axis perpendicular to the page and passing through the point P shown in picture

here is a pic of the problem:
http://imgur.com/a/c4B0X

2. Relevant equations
Torque = r * applied force

3. The attempt at a solution
Well.. I have some questions first with this one.

Am I finding the torque at the point the cable meets the crane, or at point P? I guess I really don't know much about cranes at all im not sure how they work so this adds to the confusion..

Also how am I suppose to find the length of the cable??

2. Apr 27, 2017

TomHart

The problem statement says point P.
I don't think it's necessary if you are just finding the torque from the wrecking ball around point P.

3. Apr 27, 2017

So do I just multiply r (9 meters) * the force 9800 N?

the components doesn't matter right?

4. Apr 27, 2017

TomHart

You have to take into account the angle of the force relative to the boom.

5. Apr 27, 2017

I see that the angle of the force is 5 degrees off from the ideal 90 degrees. But how do I know which component to use now? The x component makes sense to me but I'm not sure..

6. Apr 27, 2017

TomHart

I'm not sure how you are defining your x direction. But you should use the component of the 9800 N force that is perpendicular to the boom.

Edit: Look at force F2 in figure P12.45. Let's assume that force F2 is at an angle 30 degrees below horizontal. The component of the force that is perpendicular to that rod would be (F2)sin30.

7. Apr 27, 2017

Is 9800sin(30) * 9 m the same answer you got?

8. Apr 27, 2017

TomHart

30 degrees is the angle that the force makes with the horizontal, not the angle that the force makes with the boom.

Edit: What angle does the force make with the boom?

9. Apr 27, 2017

85 degrees.

so I would use the component parallel with the boom, so my answer would be

9800sin(85) * 9 m , correct?

10. Apr 27, 2017

TomHart

85 degrees is right. That is the angle between the boom and the force. And I believe 9800(sin85)(9) is the correct answer. But that is the perpendicular component, not the parallel component.