the sum of the magnitudes of two forces acting at a point is 18 and and magnitude of their resultant is 12 if the resultant is 90 degree with the force of a small animated what are the natives of Forcesdisarm the sum of the magnitude of two forces acting at a is 18 and the magnitude of their resultant is 12 if the resultant is at 90 degree with the force of a small magnitude what are the magnitudes of Forces the sum of the magnitudes of two forces acting at a point is 18 and the magnitude of their resultant is 12 if the resultant is at 90 degree with the force of a small magnitude what are the magnitude of Forces
Answers
Answer:
The sum of the magnitudes of two forces acting at a point is
18
18
and the magnitude of their resultant is
12.
12.
The resultant is at an angle of
90
o
90o
with the smaller force. We want to determine the magnitude of the forces.
Let the larger force, the smaller force and the resultant be
AB
→
,
AC
→
AB→,AC→
and
AD
→
AD→
respectively, as shown in fig 1.
Let the magnitude of the larger force be
x.
x.
It is given that
|
AB
→
|+|
AC
→
|=18
|AB→|+|AC→|=18
and
|
AD
→
|=12.
|AD→|=12.
⇒|
AB
→
|=x
⇒|AB→|=x
and
|
AC
→
|=18−x.
|AC→|=18−x.
The resultant is at an angle of
90
o
90o
with the smaller force.
⇒∠CAD=
90
o
.
⇒∠CAD=90o.
ABCD
ABCD
is a parallelogram and
AC∥BD
AC∥BD
and
AC=BD.
AC=BD.
⇒∠ADB=
90
o
⇒∠ADB=90o
and
BD
→
BD→
in fig 2
=
AC
→
=AC→
in fig 1.
It is clear that
△ADB
△ADB
in fig 2 is right angled.
⇒|
AB
→
|
2
=|
AD
→
|
2
+|
BD
→
|
2
⇒
x
2
=
12
2
+(18−x
)
2
.
⇒|AB→|2=|AD→|2+|BD→|2⇒x2=122+(18−x)2.
⇒
x
2
−(18−x
)
2
=
12
2
⇒18(2x−18)=144.
⇒x2−(18−x)2=122⇒18(2x−18)=144.
⇒2x−18=
144
18
=8⇒x=13
⇒2x−18=14418=8⇒x=13
and
18−x=5.
18−x=5.
⇒
⇒
The magnitudes of the forces are
13
13
and
5.