Question

Two forces $P$ and $Q$ have a resultant perpendicular to $P$, The Angle between the forces is

Answer 1

We have to find the angle between the forces

Step 1: Given data:

$$\alpha ={90}^{\circ }$$and $$\tan \alpha =\tan {90}^{\circ }=\mathrm{\infty }$$

The formula for the angle of the resultant vector of two vectors with respect to one vector is given as:

$\tan \alpha =\frac{Q\sin \theta }{P+Q\cos \theta }$

Where,

$P$and$Q$ are the two vectors

$$\theta$$is the angle between the vectors

$$\alpha$$is the angle between $P$ vector and the resultant vector

Step 2:

Replacing the values in the formula we get,

$$\begin{gathered} \tan \alpha =\frac{Q\sin \theta }{P+Q\cos \theta } \\ \tan 90°=\frac{Q\sin \theta }{P+Q\cos \theta } \\ \infty =\frac{Q\sin \theta }{P+Q\cos \theta } \\ P+Q\cos \theta =0 \\ \theta ={\cos }^{-1}\left(\frac{-P}{Q}\right) \end{gathered}$$

Therefore the angle between the forces is ${\cos }^{-1}\left(\frac{-P}{Q}\right)$.