Texts four forces act on a point mass as shown find the...

Texts: Four forces act on a point mass as shown. Find the Cartesian components of each force, then write the force as a Cartesian vector using the correct terminology & symbols (see your class notes).[8] Find the net force acting on the point mass by adding the above 4 force vectors.[2] F₁ = 5N F₂ = 2N F₃ = 4N F₄ = 2N

Transcript

00:02 Hi, so we are given that the four forces, the magnitudes f1 is equals to 9 newtons, then f2 is equals to 6 newtons, f3 is equals to 4 newtons and finally f4 is equals to 8 newtons.

00:22 So, we have to find the x and y component of net force and then we have to find its magnitude and direction along with the positive x axis.

00:32 So let me draw it by using the trigram.

00:35 Let's suppose this is what the vertical axis, this is the horizontal axis, this i am considering the x and of the, this is going to be y.

00:45 So according to the diagram you have been given that f1 is along the negative of x direction, then with respect to 30 degree, f2 is right over here, so this angle is given 30 degree and remaining one obviously is going to be 100 degree.

01:01 This we have given, okay.

01:03 So this making an angle with respect to f3 is given basically, with respect to f3 is making an angle of 100 degree and then this f1 making an angle of 120 degree with respect to the f4.

01:18 So we just have to find the net force.

01:23 So as you can see all will have the two more of the components.

01:28 So that we need to first, basically we just have to draw one more of the diagram so that we can write it.

01:37 So let me draw it for you.

01:39 So see, if i will try to find out this much of angle, so 130 minus of 180, so this will be goes to 70 obviously, sorry 50, it should be 50.

01:53 Then this much of angle, 180 minus 120 will become 60.

01:57 Now we can make the components here.

02:00 So as you can see, f1 is along the negative of x direction.

02:06 So here f1 will be right over there, plus one component of f2 will comes right over here, which is f2 cosine of 30.

02:17 In similar way, the vertical component will be f4 sine of 60 and f3 will have the two components.

02:25 One will be along this vertical and one will be along the horizontal.

02:32 So at this side, it will comes f3 cosine of 50 and here comes f3 cosine of 50.

02:46 But in addition to that, f2 will comes like f2 sine of 30.

02:53 So all the components i have decided here.

02:56 We just need to simplify it so that we will get the answer...

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