Year 12s: what, if anything, would discourage you from attending a uni open day? >>

M2 Hinged Frame Thing

This is from the January OCR M2 paper

A rectangular frame consists of four uniform metal rods. AB and CD are vertical and each is 40cm long and has mass 0.2kg. AD and BC are horizontal and each is 60cm long. AD has mass 0.7kg and BC has mass 0.5kg. The frame is freely hinged at E and F where E is 10cm above A, and F is 10cm below B.

(Diagram attached)

The thing I don't understand is this bit.

(i) Sketch a diagram showing the directions of the horizontal components of the forces acting on the frame at E and F.

I've marked the answer on, don't understand why they are there though/in that direction.

It'd be great if someone could also run me through the next bit too:

(ii) Calculate the magnitude of the horizontal component of the force acting on the frame at E.

Many, many thanks!

mech2.JPG10.4KB

Reply 1

Chewwy

i) imagine taking one of the hinges away. what would happen?

ii) moments from F:

E*20 = 1.2*30 + 0.2*60

Reply 2

LORDDEATH

To expand on chewwy's idea, what you do is to mentally take moments at one of the hinges (start from F). You have all clockwise moments acting from the weights of rods, so you need an anticlockwise moment so that the object would remain in equilbrium. You're told it must be horizontal, so it must be a horizontal force going to the right acting at E, which causes an anticlocwise moment. Then repeat the same procedure, taking moments at E, and for the framework to be in equilibrium, you need another anticlockwise moment again, which is a force going to the left at F.