Resultant force on a pivoted surface

Question

I have a conceptual doubt concerning the last question. So for (a) the resultant moment is 120 N anti-clockwise since the forces are acting in opposite directions, $f_1 \cdot d_1 = f_2 \cdot d_2$ thus:

$$ 600-480= 120 {\rm Nm} $$

For (b) the resultant moment is the added moments of both forces since they r acting in the same direction this:

$$ 600+480 = 1080 {\rm Nm} $$

The answer to b(ii) is conceptually confusing. I understand why the resultant force is 100 N to some extent, especially if I use the logic of contact force. As far as I know the contact force at the pivot opposes the other forces. So if 500 N is being exerted by mechanic A downwards contact force is 500 N upwards at the pivot.

And if 400 N is being exerted by mechanic B upwards then 400 N is being exerted downwards from the pivot.

Therefore 500 N upwards- 400 N downwards gives me 100 N p force at the pivot upwards. That means a resultant force of 100 N acts downwards which we can intuitively say acts from the left end of the spanner since the moment arises from that direction.

The mark scheme for Cambridge igcse physics says the answer is 100 N. But my question is if the resultant force is 100 N that would mean the resultant moment is 120 N m which would be incorrect since we just figured out that the resultant moment is 1080 N (which the mark scheme says is correct).

So what concept am I missing here, it doesn’t make much sense to me.

Answer 1

Perhaps to resolve your uncertainty you should consider adding two $500\,\rm N$ forces (red and blue) equal in magnitude and opposite in direction acting at pivot $P$ and do the same with two $400\,\rm N$ forces (green and pink).

You now have two couples (red and green) which only produce a rotation as the net force is zero and a net force acting at pivot $P$ being the sum of two forces acting at $P$ (blue and pink) and no torque about pivot $P$.

Answer 2

Actually, Resultant Force and Resultant Moments are both different things. Resultant Force is summation of all forces in linear direction, but Resultant moment is a summation of moments due to all the forces.

Answer 3

In the first case, one moment (torque) is clockwise and the other is CCW (relative to the nut). In the second case both are CCW.