00:01
Hello everyone, let's look at the given problem and in this problem we have been given vectors at certain distances as known in this figure where the magnitude of force a is equal to 12 newton and force b is 11 newton and force c is 23 newton and the distance of a point a from o is equal to 9 .3 meter and point b is at 3 .9 meter and point c is at 2 .1 meter from the point o.
00:42
Now we need to find the total tall acting at the point o.
00:47
So as we know that our tau is given as vector r cross vector f where r is the position vector so this taught tau can be written as r times f times sine theta and this theta is the angle between the vector vector vector and vector f so we will be using this formulae to solve this question so first upon we will calculate the torque for force a so here we can see that there is a and at this point force is acting in this direction and this angle is 135 degree therefore if we extend this we will get this angle as 45 degree and this will be our position vector now if we calculate the torque for this f a this will be equal to oa that is r vector and then f a is the force and this will be sign 45 tp and the direction of this talk will be in so this force will try to move in this direction so this will be in counterclockwise so if we solve this we will get down a is equal to so this way is 9 .3 multiplied by 12 multiplied by sine 45 is 1 divided by 2 and this will be in newton meter so finally we will get tau a is equal to 78 .9 newton meter in counter clockwise direction so now we will calculate torque 4.
02:27
B so if you see the figure the b is acting at 90 degree so this is this is force b and this is acting at 9080.
02:40
So here we can write tau b will be equal to ob vector magnitude and fb vector magnitude and sign 90 degree.
02:50
This force will try to create a torque in clockwise direction.
02:55
So we will take this in negative side.
02:57
So this will be tau b is equal to negative of ob is 3 .9 meter multiplied by fv is 11 newton and sine 90 is 1 this will be newton meter so if you saw this we will get tau is equal to negative of 43 .9 newton meter and this is in clockwise direction similarly we will come at 4.
03:25
C so here if you see the figure then there is a line and factor c is acting at 160 degree so this angle will be 20 degree and this is our oc vector.
03:42
So now if we find the torque due to c, this will be oc vector multiplied by fc.
03:48
So this is fc vector multiplied by sine 20...