- #1
gnits
- 137
- 46
- Homework Statement
- To prove that three forces are in equilibrium
- Relevant Equations
- Equating of forces
Could I please ask for help regarding the following question:
D, E and F are the midpoints of the sides QR, RP and PQ respectively of triangle PQR whose circumcenter is O. Forces of magnitude kQR, kRP and kPQ act at O in directions ##\overrightarrow{OD}##, ##\overrightarrow{OE}## and ##\overrightarrow{OF}## respectively.
Prove that the forces are in equilibrium.
I am allowed to make use of the following fact, (although I am free to answer the question any other way):
With both forces going away from A we have:
##p\overrightarrow{AB}## + ##q\overrightarrow{AC}## = ##(p+q)\overrightarrow{AD}##
where
##BD:DC = q:p##
Here's a diagram for the problem (the green stuff is referenced in my solution below where I attempt to apply the above fact).
I was hoping to show that the kPQ and kQR forces combined to give a force which was opposite (so ##\overrightarrow{OX}## would be opposite to ##\overrightarrow{OE}## ) and of equal size to the kRP force by using the above fact. Well straight off I see that this would give a force of magnitude k(QR + PQ) which I would need to be equal to kRP, and I can't see how that can be so.
Thanks for any help,
Mitch.
D, E and F are the midpoints of the sides QR, RP and PQ respectively of triangle PQR whose circumcenter is O. Forces of magnitude kQR, kRP and kPQ act at O in directions ##\overrightarrow{OD}##, ##\overrightarrow{OE}## and ##\overrightarrow{OF}## respectively.
Prove that the forces are in equilibrium.
I am allowed to make use of the following fact, (although I am free to answer the question any other way):
With both forces going away from A we have:
##p\overrightarrow{AB}## + ##q\overrightarrow{AC}## = ##(p+q)\overrightarrow{AD}##
where
##BD:DC = q:p##
Here's a diagram for the problem (the green stuff is referenced in my solution below where I attempt to apply the above fact).
I was hoping to show that the kPQ and kQR forces combined to give a force which was opposite (so ##\overrightarrow{OX}## would be opposite to ##\overrightarrow{OE}## ) and of equal size to the kRP force by using the above fact. Well straight off I see that this would give a force of magnitude k(QR + PQ) which I would need to be equal to kRP, and I can't see how that can be so.
Thanks for any help,
Mitch.