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sumof two forces at a point is 16N.IF THE RESULTANT IS NORMAL TO SMALLER FORCE AND HAVE A MAGN ITUDE 8N. the two forces are ? 6 and 10n how

sumof two forces at a point is 16N.IF THE RESULTANT IS NORMAL TO SMALLER FORCE AND HAVE A MAGN
ITUDE 8N. the two forces are ? 6 and 10n how

Grade:11

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
assume smaller force is fsand larger force is fl and resultant is fr. as given in the question, when we will form the parallelogram the let acute angle between fs and fl is theta. so these two eqns will be formed-
fs=fl*cos(theta)...1
fr=fi*sin(theta)...2
fs+fl=16...3 fr=8
from 3 and 1-
16=fl(1+cos(theta))...4
by 2/4 0.5=sin(theta)/1+cos(theta)

.5=2sin(theta/2)*cos(theta/2)/2cos^2(theta/2)
0.5=tan(theta/2)
theta=2tan^-1(.5)=tan^-1(2*.5/1-.25)
=>tan(theta)=4/3
sin(theta)=4/5
cos(theta)=3/5
so fl=8*5/4=10N and fs=6N


sher mohammad
b.tech iit delhi
faculty, askiitians

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