Two forces 𝐏 and 𝐐 are applied as shown at point A of a hook...

Two forces $\mathbf{P}$ and $\mathbf{Q}$ are applied as shown at point $A$ of a hook support. Knowing that $P=75 \mathrm{~N}$ and $Q=125 \mathrm{~N},$ determine graphically the magnitude and direction of their resultant using ( $a$ ) the parallelogram $\mathrm{law},(b)$ the triangle rule.

Transcript

00:01 Hello and welcome to this video solution of numerate.

00:03 So here we are given two forces p and q that are applied at the point a on a hook as shown in this diagram right.

00:12 This is the point a.

00:19 Now you have to determine graphically the magnitude and the direction of the resultant using a, the parallelogram law and b, the triangle rule.

00:29 So what you can do is you need to draw these two vectors in a graph paper let's say.

00:34 So you cannot draw actually 75 newton or 125 newton.

00:38 So what you can do is you need to take a scaling factor.

00:41 So first what you can do is you can take let's say 10 newton that will be equivalent to 1 centimeter right.

00:50 So this will be 75 newton will be equivalent to 7 .5 centimeters and 125 newton that will be equivalent to 12 .5 centimeters right.

01:01 Now what you can do is you can draw the same vectors in your graph paper sort of like this.

01:06 So this is vector p this length will be 7 .5 centimeters and you will be having vector q that will be 12 .5 centimeters right.

01:21 The angle will remain the same between them which is 20 and 35 from the vertical.

01:26 These angles will remain the same.

01:28 Now from parallelograms law what you can do is you can just draw parallelogram with the same vectors on the other sides right on the adjacent sides let's say.

01:39 So this q vector you need to translate it on the other side of p sort of like this and the same p vector around this or you don't need the arrow signs here.

01:50 You can only draw simple lines right just to form a parallelogram.

01:57 Now the resultant will be the this is point a right and this is point b let's say.

02:03 The resultant will be the line joining between the point a and b or the diagonal of this parallelogram...

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