 #1
rudransh verma
Gold Member
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 91
 Homework Statement:

Three forces causes a net acceleration of ##3 \frac {m}{sec^2}## . Two of the forces ##F_1## and ##F_2## are 10N and 20N. Find the ##F_3## in unit vector notation?
Mass of the body is 2 kg.
 Relevant Equations:

##\vec F= m\vec a##
##\vec{F_1} +\vec{F_2}+\vec{F_3} = m \vec a##
x component of ##F_3##
##F_{3x}= m a_x F_{1x}F_{2x}##
= ##ma\cos 50F_1\cos(150)F_2\cos90##
y component of ##F_3##
##F_{3y}= m a_yF_{1y}F_{2y}##
=##ma\sin50F_1\sin(150)F_2\sin90##
And so on…
My question how we can represent it in diagram ##F_1\sin(150)##. I suppose what is ##\sin(150)## : ##\sin(30)## and 30 is measured from position X axis. So what is the component now . Is it now in Forth Quadrant from 3rd.
I can understand the component ##F_1\sin30## or ##F_1\cos30## in diagram but the above component, I don’t.
I could have done it via reference angle taking a right triangle in each quadrant and taking acute angles and put a sign accordingly to each component after calculating magnitude of each component. But I choose to do it more systematically by textbook way.
I was told you can do it by unit circle convention. That’s what I am aiming for, for doing all the vector questions. Taking all the angles from + direction of xaxis and straight away putting in ##\cos and \sin##. In this way I don’t have to worry about the signs. It is dealt automatically.
##F_{3x}= m a_x F_{1x}F_{2x}##
= ##ma\cos 50F_1\cos(150)F_2\cos90##
y component of ##F_3##
##F_{3y}= m a_yF_{1y}F_{2y}##
=##ma\sin50F_1\sin(150)F_2\sin90##
And so on…
My question how we can represent it in diagram ##F_1\sin(150)##. I suppose what is ##\sin(150)## : ##\sin(30)## and 30 is measured from position X axis. So what is the component now . Is it now in Forth Quadrant from 3rd.
I can understand the component ##F_1\sin30## or ##F_1\cos30## in diagram but the above component, I don’t.
I could have done it via reference angle taking a right triangle in each quadrant and taking acute angles and put a sign accordingly to each component after calculating magnitude of each component. But I choose to do it more systematically by textbook way.
I was told you can do it by unit circle convention. That’s what I am aiming for, for doing all the vector questions. Taking all the angles from + direction of xaxis and straight away putting in ##\cos and \sin##. In this way I don’t have to worry about the signs. It is dealt automatically.
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