Calculating the Moment of a Resultant Force

  • Thread starter Thread starter physicsss
  • Start date Start date
  • Tags Tags
    Moment Point
Click For Summary

Homework Help Overview

The discussion revolves around calculating the moment of a resultant force exerted on a pulley by a rope system, specifically focusing on the forces involved and their vector representations. The context includes the setup of a telephone cable and the tensions in the ropes involved.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss drawing free-body diagrams and calculating resultant forces from tensions in the ropes. There are questions about the orientation of the plane and the angles involved. Some participants share their calculations of resultant forces and moments, while others express uncertainty about the formulas used for distances and moments.

Discussion Status

The discussion is active, with participants sharing various calculations and questioning the accuracy of their approaches. There is a mix of approximations and corrections being made, indicating an ongoing exploration of the problem without a clear consensus on the final results.

Contextual Notes

Some participants express confusion regarding the orientation of the plane and the application of formulas for calculating distances from points to lines. There is also mention of specific resources being referenced for clarification.

physicsss
Messages
319
Reaction score
0
Before a telephone cable is strung, rope BAC is tied to the stake at B and is passed over a pulley at A. Knowing that portion AC of the rope lies in a place parallel to the xy plane and that the tension T in the rope is 124 N, determine the moment about O of the resultant force exerted on the pulley by the rope.

How do I find the resultant force?
 

Attachments

  • Picture1.jpg
    Picture1.jpg
    12.4 KB · Views: 787
Physics news on Phys.org
Draw a free-body diagram.
Consider the plane BAC, which is parallel to the x-y plane.
You have tensions in the ropes AB and AC. You know, or can work out, the angle between the two tensions. You should now be able to work out the resultant of the two tensions.
 
I don't think plane BAC is parallel to the x-y plane. Only line AC is.
 
You're right. I should wear my specs more often!

Mmmm ...
 
So F from A to B is 124(1.5m i - 9m j + 1.8m k)/sqrt(1.5m^2+9m^2+1.8m^2)
and from F from A to C is 124N cos(10) i +124N*sin(10) j ?
 
Last edited:
I'm doing it by vectors, atm, and I get the resultant force = 176N. (not checked)

I've got the resultant as a vector. But I cant' remember the formula for distance to a line from a point ( e.g. the origin). Any ideas ??
 
My resultant force was 174.5 N, close enough?
 
yeah, I approximated a bit, just to work through :)
 
I got 137 i - 142 j + 1393 k for the moment...
 
  • #10
The magnitude of your moment is about 1407.
I get about 1250!

I think I'm doing something wrong with this formula I have for the distance from a point to a line :(
 
  • #11
Oops...it's 118 i - 142 j + 1279 k...my mistake...
 
  • #12
Well, then that could be about right. I got 1250 using the value of 176.17 for the resultant force.

I've still got a niggling point about the formala I used for the distance though.
Have you ever seen http://ericvesey.com/geometry/vectors.pdf#nameddest=10 - bottom of page 5.

I tried to use it to compute the distance of the point B, in your sketch, from the origin and got zero!
 
Last edited by a moderator:
  • #13
Hmm forget what I said above...I didn't do it that way, I crossed the distance from the origin to the pulley with the resultance force in its i, j, k components:

(9 j + 1 k) X (142 i - 98.468 j + 24 k), and the resultant is 1325...
 

Similar threads

  • · Replies 33 ·
2
Replies
33
Views
8K
  • · Replies 8 ·
Replies
8
Views
5K
Replies
8
Views
1K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 3 ·
Replies
3
Views
14K
Replies
4
Views
3K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K