How Do You Calculate the Moment in a Force-Couple System at a Pivot Point?

[zeralda21]

Homework Statement

A force F of magnitude 50 N is exerted on the automobile parking-brake lever at the position x=250 mm. Replace the force by an equivalent force-couple system at the pivot point O.

Picture: http://i.imgur.com/dJGtvAo.png

Homework Equations

M=F*d

The Attempt at a Solution

I have replaced the force by an equivalent force-system at O so I now the exact same force F(both magnitude and direction) but at O. Now I want to find the moment which is given by M=Force*distance. The distance I need is the closest distance between O and the "moment-point". For simplicity I instead try to find the distance between O and Fcos20. But I have problems finding it.

 

[tiny-tim]

hi zeralda21!

The distance I need is the closest distance between O and the "moment-point".

no, it's the closest distance between O and the line of the force

probably easiest to start by extending the left-hand part until it reaches the line of F, and finding the total length of that

 

[zeralda21]

hi zeralda21!


no, it's the closest distance between O and the line of the force

probably easiest to start by extending the left-hand part until it reaches the line of F, and finding the total length of that

Ouch, that is actually what i meant. But the closest distance is therefore the horizontal distance from O to Fcos(20), no? I'm not sure what you mean. Extend it as:

0.1m+xcot15 ?

 

[tiny-tim]

hi zeralda21!

But the closest distance is therefore the horizontal distance from O to Fcos(20), no? I'm not sure what you mean. Extend it as:

0.1m+xcot15 ?

on second thoughts, i don't think that works

try it this way …

draw a line OG parallel to the line of F

then the distance is the sum of the perpendicular distances from that dot in the middle to the line of F, and from that dot in the middle to OG