Observe the following diagram. Calculate the mass of the stone using the parallelogram law of vector addition
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Explanation:
Parallelogram Law of Vectors states that, If two vectors acting simultaneously at a point can be represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing
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Physics
Motion in a Plane
Mathematical Operations on Vectors
Derive an expression for th...
PHYSICS
Derive an expression for the magnitude and direction of the resultant vector using parallelogram law
December 27, 2019avatar
Munny Kaul
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Parallelogram law states that if two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.
In the figure
P
and
Q
are two vectors.with magnitudes equal to length OA and OB respectively and making angle θ between them. Complete the parallelogram, OACB,
Join diagonal OC , that makes angle α with vector
P
.
According to parallelogram law of vectors the resultant is represented by the diagonal passing through the point of contact of two vectors.
To find the magnitude of resultant , produce a perpendicular CD to meet OA produced to D.
From △ OCD,
OC
2
=OD
2
+CD
2
Now
C
D=
A
C sinθ=
Q
sinθ
AD=
A
Ccosθ=
Q
cosθ
O
D=
O
A+
A
D=
P
+
Q
cosθ
Putting these values and representing resultant vector OC by
R
, magnitude of the resultant is given by
R
2
=(
P
+
Q
cosθ)
2
+(
Q
sinθ)
2
=
P
2
+
Q
2
+2
P
Q
cosθ
In △ OCD,
tanα=
OD
CD
=
P
+
Q
cosθ
Q
sinθ
Resultant acts in the direction making an angle α=tan
−1
(
P
+
Q
cosθ
Q
sinθ
) with direction of vector P .
solution