Question

two forces P and Q pass through a point A which is 4 ft to the right of and 3 ft above a moment center O. force P is 200 lb directed up to the right at 30degrees with the horizontal and force Q is 100 lb directed up to the left at 60degrees with the horizontal, determine the moment of the resultant of these two forces with respect to O.

Answer 1

we have to use \[\tau=F \times r \]
first of all we need to break the forces into their components-horizontal and vertical
here we use the formula \[\tau=F _{perpendicular}\times r\]
or \[\tau=F \times r_{perpendicular}\]
both are the same
the formula says that we need to multiply the magnitudes of the force and the radius vector which are perpendicular
this is the original condition:

and when we break the forces into horizontal and vertical components, this becomes the situation:

we choose the reference point to be the moment center O
now we multiply the force components with their perpendicular distances from the moment center.
then we determine the direction of the moments due to each component and then add or subtract the moments accordingly and that is the final answer!
I may not be very clear so please feel free to ask anything about this

Answer 2

how can i determine the sign?im confuse of that...thanks for ur answer by the way..!

Answer 3

thanks for the medal!
we can determine the sign by using the cross product rule
we know, torque is the cross product of radius and the force (the sequence of radius and force is important)
you put your fingers in the direction of the radius vector and then curl them towards the force vector and then outstretch your thumb. Then your thumb shows the direction of the moment.

Answer 4

well where are you from?

Answer 5

from philippines..is that the right hand rule u mean?

Answer 6

my answer is -379.79 lb-ft

Answer 7

yes that's the right hand rule
and by the way i am from india

Answer 8

i'm working on the answer

Answer 9

i got the answer=76.795

Answer 10

here my drawing and answer

Answer 11

okay!
i made the wrong drawing

Answer 12

it should be P(y)(4) + Q(y)(4) + Q(x)(3) - P(x)(3)

Answer 13

why negative px?is that because of direction of x is negative in P?

Answer 14

is that mean the answer is positive 379.79lb-ft

Answer 15

i assumed the direction into the plane to be negative and direction and the direction out of the plane to be positive
the right hand thumb rule

Answer 16

so whats ur answer?

Answer 17

my answer is 376.7949
very close to yours

Answer 18

same answer

Answer 19

okay then maybe it's correct

Answer 20

okay i got it you took into account the direction of the forces and i just manipulated it without taking in account the negative sign of the Qx component

Answer 21

what do u mean?

Answer 22

the Qx component is directing towards left so it's sign is negative according to the sign convention

Answer 23

yes thats what i understand...thats what im asking u..is that correct?is there a general rule for the sign?some says its positive if clockwise and negative when counterclockwise?some says because of direction and u said use a right hand rule...

Answer 24

look just forget it!
use the right hand rule properly and you'll get the correct answer
choose one direction to be positive and the other to be negative
generally if not specified in the question, we assume the outward direction to be positive and vice-versa.
i'll be back in 15 mins. i have to bath

Answer 25

thanks for the medal @SurpriseBreeze

Answer 26

:)