00:01
Hello students, we are given the following diagram.
00:03
In the free body diagram, first the force of 700 newton can be resolved into its x and y components.
00:10
Let's say this is angle theta then this component will be 700 cos theta and this component will be 700 sin theta.
00:21
Further, the force of 2000 newton can also be resolved into its x and y components.
00:28
Let's say this is angle alpha then this component will be 2000 cos alpha and this component will be 2000 sin alpha.
00:44
Now the normal reaction of b acts in the upward direction.
00:51
Let's say it is equal to rb and the normal reaction of a, since it is attached to the rod, the normal reaction, the reaction of a can have two components, that is one is the x component and one is the y component.
01:12
So let's say these components are rax and ray, that is reaction of a along the x direction and reaction of a along the y direction.
01:28
So the resultant reaction of a will be somewhat in this direction, that is ra and let's say the reaction makes an angle beta with the negative x -axis in the clockwise direction.
01:43
Now net force along the x direction is equal to zero which gives us minus 700 sin theta plus 2000 sin alpha minus rax is equal to zero.
02:04
Now from the figure we can write the following trigonometric ratios tan theta is equal to 4 by 3 sin theta equals to 4 by 5 cos theta is equal to 3 by 5 tan alpha is equal to 5 by 12 sin alpha equals to 5 by 13 and cos alpha is equal to 12 by 13.
02:42
Now using these values in the equation of net force equals to zero we get rax equals to minus 700 into 4 by 5 plus 2000 into 5 by 13.
03:06
This gives us the value of the x component of the reaction due to a that is rax equals to 209 .23 newtons and it is in the negative x direction...