The largest resultant of two forces P and Q is 31N and the least resultant is 17N. What is
the resultant if P and Q act at right angle?
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2
Answer:
Let the two forces are
P
and
Q
N and
P
>
Q
Given that the resultant of 2 forces at right angles is 17 N, we can write
P
2
+
Q
2
=
17
2
...
.
.
(
1
)
Again it is also given that the maximum resultant is
23
N.The resultant of two forces becomes maximu when the angle between them is zero. So the magnitude of the resultant will be sum of the magnitudes of two vectors.
So we can also write
P
+
Q
=
23
...
...
(
2
)
Now
(
P
+
Q
)
2
+
(
P
−
Q
)
2
=
2
(
P
2
+
Q
2
)
⇒
23
2
+
(
P
−
Q
)
2
=
2
×
17
2
⇒
P
−
Q
=
√
2
×
17
2
−
23
2
=
√
578
−
529
=
√
49
=
7
N
So
P
−
Q
=
7
...
.
.
(
3
)
Adding (2) and (3) we get
2
P
=
30
⇒
P
=
15
N
So greater force
P
=
15
N
Explanation:
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