How Does Rotating Forces Through Equal Angles Affect Their Resultant?

[batballbat]

Homework Statement

Two given forces act at two given points of a body; if they are turned round those points in the same direction through any two equal angles, show that their resultant will always pass through a fixed point.
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Homework Equations

The Attempt at a Solution

i tried but could not make any progress with the problem

 

[tiny-tim]

hi batballbat!

the first thing to do is to find where that point is …

so try the two simplest cases, one in which the first force points along AB, and one in which the second force points along AB …

what do you get? ​

 

[tiny-tim]

if two forces act on different points of a body then at which point does the resultant act?

hint: add the two forces, then subtract the resultant …

that must be zero, and in particular, its moment about any point must be zero

 

[batballbat]

i didnt get u

 

[tiny-tim]

if you have a force F along the line AP, and another force F along the line BQ,

and if the resultant of F and G is H,

the the resultant of F G and -H must be zero,

so in particular the moment of F + G - H about any point must be zero …

so what point must H go through?​

 

[batballbat]

i have the problem of adding two vectors not acting at the same point. can u give me a general solution?

 

[tiny-tim]

the point of application of the force does not matter,

only the line of application of the force matters …

if a force is acting at a point A, it's the same as if it was acting at any other point on the line through A in the direction of the force

 

[batballbat]

ok so the resultant acts along AD

 

[tiny-tim]

ok so the resultant acts along AD

what's D ?? there isn't a D !

go back to my previous question …

try the two simplest cases, one in which the first force points along AB, and one in which the second force points along AB

 

[batballbat]

is it one of the two given points on the body?
just give me an answer if u are not allowed to give a solution