Edexcel Mechanics Hinges

Hi I’m very confused on a question, if we have a rod that it attached to a vertical wall and this rod is held in horizontal position by a rope, then why does the resultant force where the rod is attached to the wall act diagonally?

For example in question 1

https://www.examsolutions.net/tutorials/exam-questions-moment-of-a-non-perpendicular-force/?level=A-Level&board=Edexcel&module=Mechanics%20A-Level&topic=1645

Solution;

https://youtu.be/3JXw_I9DM6c

Any help would be appreciated, thanks!

(edited 4 years ago)

Reply 1

mqb2766

Original post by penelopehills

Vertical: At A, friction (wall) must be acting upwards as the plank is not rotating about B. Otherwise the COM of the plank (and P) would cause the plank to rotate anticlockwise (downwards) about B.
Horizontal: The rope's tension pulls the plank into the wall at A (this must be the case as its the perpendicular force which causes the vertical friction) and hence the wall pushes back with the same force at A
So at A, the wall is reacting upwards and to the right, so the reaction force at A is diagonal in quadrant 1.

(edited 4 years ago)

Reply 2

David Getling

Let's look at it like this. As the plank isn't rotating there must be a moment due to the tension in the rope. But the vertical component of the tension isn't equal to the mass of P plus the mass of plank (times g, of course). Therefore it must be made up at the hinge. Now there is also a horizontal component from the rope, pulling the plank towards the wall. The only thing that can oppose this is a horizontal component from the hinge.

So the hinge has both a horizontal and a vertical component. When we add these the resultant force at the hinge acts diagonally.

Reply 3

REUSueeufn#2848

Original post by David Getling

Ah ok I get the bit about the force opposing the horizontal component of the tension, however why can the vertical component tension not be equal to the mass of plank and P? Probably a silly question, but could this ever be the case? Thanks!

Reply 4

mqb2766

Original post by penelopehills

If you took moments about A, the COM (and P) would be balanced by the upwards tension. However, its the moments that are balanced. So assuming no P (simplistic) and the COM is at the center of the plank, then the upwards forces at A (friction on wall) and B (upwards tension) are both equal to half the weight of the plank. The 1/2 comes because the COM is halfway along the plank, assuming its uniform.

Reply 5

Justvisited

Original post by penelopehills

Answer given above. Let us know if there's anything in the question you still can't do.

Reply 6

REUSueeufn#2848

So the resultant diagonal at A comes from resolving the frictional and reaction force of the wall at A then? Ah I’m sorry for how stupid I come across I really struggle with mechanics /::

Reply 7

RDKGames

Study Forum Helper

Original post by penelopehills

So the resultant diagonal at A comes from resolving the frictional and reaction force of the wall at A then? Ah I’m sorry for how stupid I come across I really struggle with mechanics /::

The resultant force at A is acting diagonally. It is made up of TWO components, a horizontal one (representing the normal reaction of the wall on the rod) and a vertical one (representing the frictional force between the rod and the wall)

In the question's part (c), this diagonal force is at an angle

\beta

to the horizontal. By drawing out the components, you construct a right-angled triangle, and then should quickly realise that

\tan \beta = \dfrac{\mathrm{opposite}}{ \mathrm{adjacent} } = \dfrac{\text{vertical force}}{\text{horizontal force}}

(edited 4 years ago)

Reply 8

David Getling

Original post by penelopehills

So the resultant diagonal at A comes from resolving the frictional and reaction force of the wall at A then? Ah I’m sorry for how stupid I come across I really struggle with mechanics /::

Don't feel bad, a lot of students struggle with mechanics, and often it's not taught very well. You are right now. We get vertical friction because of the horizontal reaction. Then when we add the vertical friction and horizontal reaction our resultant is diagonal.