Laws of Motion -01- Resolve A Weight Vector

Resolve a weight of 100 N in two directions which are parallel and perpendicular to a slope inclined at 60° to the horizontal.   #vector

Transcript

00:00Hi friends, welcome Saturday morning with full enthusiasm, passion and love.

00:07The question on this screen is about component vectors.

00:11A block with a certain weight is on an inclined surface.

00:16We are asked to decompose the weight vector into two directions,

00:20one parallel and the other perpendicular to the inclined surface.

00:27Let's answer this question easily.

00:32Before going any further, just draw the weight as a vertical arrow downwards as W.

00:39Weight is a vector quantity.

00:41Vector quantities can be resolved into several vector components.

00:46What is certain is that when all the vector components are added together,

00:50the original vector will be obtained.

00:54The first component is a vector that is parallel to the inclined surface.

00:59Just draw a vector starting from the origin of vector W,

01:02which coincides with the inclined surface line.

01:06We can estimate the length of this vector.

01:09It doesn't matter.

01:11This is a vector that is parallel to the inclined surface.

01:18The second component is a vector that is perpendicular to the inclined surface.

01:23Like the previous process, draw a vector that starts from the starting point of the vector W

01:28that is perpendicular to the inclined surface.

01:32Don't think about the length of this vector.

01:35Certainly, vector W is the diagonal of the plane of the box formed by the two component vectors.

01:43Now, we will analyse the angle of the vector.

01:48The angle of the inclined surface is 60 degrees.

01:54Consider this triangle.

01:56It is a right triangle.

01:59Thus, this angle is 30 degrees.

02:05Using the concept of trigonometry, the cosine of 30 degrees is W parallel over W.

02:13From here, W parallel is equal to W cosine 30.

02:20In the question sheet, the value of W is 100 newtons

02:24and the cosine of 30 degrees is half the root of 3.

02:28So W parallel is 50 root 3 newtons.

02:34Next, the sine of 30 degrees is W perpendicular over W.

02:41From here, W perpendicular is equal to W sine 30 degrees.

02:48Plugging in the values of W and sine, W perpendicular is equal to 50 newtons.

02:56This is the component of the weight vector asked by the question.

03:01Happy learning everyone!