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OCR M3: Systems of Rigid Objects - Question 2

Hi, I am not sure how to solve this question, any help is appreciated.

Two uniform rods XY and YZ, each of weight 20N and length 80cm, are connected by a smooth pin joint at Y. They rest symmetrically on two smooth pegs P and Q at the same level, with angle XYZ =90 degrees. Show that P and Q are approximately 28 cm apart and find the magnitude of the force from the pin on each rod.

Thanks for the help
Original post by HashBrowns
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Diagram.

Then what are you able to deduce from the question?
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Both reaction forces are equal? And how would I know which direction they would be in?
Original post by HashBrowns
Both reaction forces are equal? And how would I know which direction they would be in?


Which reaction forces are you refering to?

Edit: Hinge or pegs?
(edited 10 years ago)
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Pegs
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Original post by ghostwalker
Which reaction forces are you refering to?

Edit: Hinge or pegs?


Pegs
Original post by HashBrowns
Pegs


And the pegs are smooth, so what direction is the reaction?

PS: I presume you've drawn a diagram.
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Original post by ghostwalker
And the pegs are smooth, so what direction is the reaction?

PS: I presume you've drawn a diagram.


I think it would be perpendicular to the rods.
Original post by HashBrowns
I think it would be perpendicular to the rods.


Yep. It can't have any component along the rod, as the peg is smooth.
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Original post by ghostwalker
Yep. It can't have any component along the rod, as the peg is smooth.


How about the reaction forces at the hinge?
Original post by HashBrowns
How about the reaction forces at the hinge?


Bearing in mind the symmetry of the situation, consider, can there be a vertical component to the reaction at the pin?
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Original post by ghostwalker
Bearing in mind the symmetry of the situation, consider, can there be a vertical component to the reaction at the pin?


I think there isn't a vertical component as otherwise the forces wouldn't balance out considering each rod separately. Not sure though.
Original post by HashBrowns
I think there isn't a vertical component as otherwise the forces wouldn't balance out considering each rod separately. Not sure though.


That's correct.

If there was a vertical component in one rod, there would have to be a similar vertical component in the other by symmetry, but equally there would have to be an equal and opposite force, by Newton's Laws.

So, V=V and V=-V hence V=0.

So only a horizontal force exists.
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Original post by ghostwalker
That's correct.

If there was a vertical component in one rod, there would have to be a similar vertical component in the other by symmetry, but equally there would have to be an equal and opposite force, by Newton's Laws.

So, V=V and V=-V hence V=0.

So only a horizontal force exists.


I got F = 20N, and think this is correct. Could you answer the question on my new thread? Thank you very much for the help.
Original post by HashBrowns
I got F = 20N, and think this is correct. Could you answer the question on my new thread? Thank you very much for the help.


Agreed.

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