Help with A level maths questions

I have the answer for the 1st part of the question I just need help with the 2nd part

4. Fig. 3 shows a rod AB which is 0.9m long and hangs vertically from a smooth hinge at A. The rod can rotate about A in a vertical plane. Forces of 100N and 60N act at right angles to AB in this plane. Their points of application are 0.3 m and 0.75 m respectively below A.
(a) Find the combined moment of these forces about A.
(b) The rod is held in equilibrium by a force of FN which is also at right angles to the rod in the same vertical plane.

Find the least possible value of F

(edited 2 months ago)

Reply 2

mqb2766

Original post by KindPot

4. Fig. 3 shows a rod AB which is 0.9m long and hangs vertically from a smooth hinge at A. The rod can rotate about A in a vertical plane. Forces of 100N and GON act at right angles to AB in this plane. Their points of application are 0.3 m and 0.75 m respectively below A.
(a) Find the combined moment of these forces about A.
(b) The rod is held in equilibrium by a force of FN which is also at right angles to the rod in the same vertical plane.

Find the least possible value of F

Not sure about the GON force, but the least force for F will be when it occurs where on the rod?

Reply 3

mathcool

You have not shown figure 3.

Assuming that you got the resultant moment part (a),

For part (b), you have to apply F at right angle to the rod in the same vertical plane at, let's say, distance D from the hinge.

Since the application of F is keeping the rod in equilibrium (F has to create a moment in the directly opposite direction to that of in part (a)).

So,
F x D = moment in part (a) (which is a number, a constant)

F = moment in part (a) (which is a number, a constant) / D

Now, for F to be the least, D has to be as large as possible.

Since the F can only be applied on the rod, the largest possible D is the length of the rod from A (i.e. hinge).