# 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
Original post by KindPot
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.

1.

﻿﻿﻿﻿Find the least possible value of F

(edited 5 months ago)
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.

1.

﻿﻿﻿﻿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?
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).