Question

The resultant of 2 forces at right angles is 17 N.if the maximum resultant is 23 N,then what is the value of the greater force?

Answer 1

Greater force `P=15`N

Explanation:

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=2xx17^2`

`=>P-Q=sqrt(2xx17^2-23^2)=sqrt(578-529)=sqrt49=7N`

So `P-Q=7.....(3)`

Adding (2) and (3) we get

`2P=30`

`=>P=15`N

So greater force `P=15`N