Calculating Reaction Forces in a Plank System: Bill and Dave

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In summary, the plasterers Bill and Dave each stand on a plank supported at two points, C and E. At C, Bill is 0.5m from A and at E, Dave is 1.5m from F. At F, both plasterers are 1m from B. The plank is in equilibrium, but both plasterers are incorrect in their calculations of S.
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Homework Statement


Two plasterers Bill and Dave of mass 45kg and 65kg respectively stand on a unofrm plan ABCDEF of length 4m and mass 40kg. The plank is supported at C and E where C is 1m from A and E is 1m from F. Plasterer Bill stands at B which is 0.5m from A and plasterer Dave stands at D which is 1.5m from F.
a) Draw a diagram showing the above information
b) Find the reaction at each support, giving your answers in N to 1 decimal place.


Homework Equations


http://img164.imageshack.us/img164/9263/drawnqf5.jpg [Broken]
I drew this on paint, seems to be correct. Thats a) done.

The Attempt at a Solution


The question dosen't state anything about Equilbirum, but here's what I done:
m(R):
0.5 x 45g + S = 40g + 1.5 x 65g
S = 40g + 97.5g - 22.5g
S = 1127N

Sub this into:
S + R = 150g
R = 150g - 1127
R = 343N.

However they are both completely wrong, I assume I am going wrong with thinking it is in equilbrium. Since it isn't, I'm not too sure on where to start.
Any hints/help is very appreciated =)!

Thank you.
 
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  • #2
I think it is correct to assume that the plank is in equilibrium, since it says it is supported at C and E.

How have you set up your equations? The way to proceed in this sort of question is to take moments about a pivot, set the anticlockwise moments equal to the clockwise moments, and then obtain an equation. Now, to find S, say, where do you think you should take the pivot to be?
 
  • #3
cristo said:
I think it is correct to assume that the plank is in equilibrium, since it says it is supported at C and E.

How have you set up your equations? The way to proceed in this sort of question is to take moments about a pivot, set the anticlockwise moments equal to the clockwise moments, and then obtain an equation. Now, to find S, say, where do you think you should take the pivot to be?


Ahhh, I just found my mistake.
I just put S, and S is 2m away from R.

m(R):
0.5 x 45g + 2S = 40g + 1.5 x 65g
2S = 40g + 97.5g - 22.5g
2S = 1127N
S = 1127/2
S = 563.5N

R = 150g - 563.5
R = 906.5N

Those are the correct answers, I looked at it a few times and missed this out every time, THANK YOU for the help =)
 
  • #4
Lavace said:
Ahhh, I just found my mistake.
I just put S, and S is 2m away from R.

m(R):
0.5 x 45g + 2S = 40g + 1.5 x 65g
2S = 40g + 97.5g - 22.5g
2S = 1127N
S = 1127/2
S = 563.5N

R = 150g - 563.5
R = 906.5N

Those are the correct answers, I looked at it a few times and missed this out every time, THANK YOU for the help =)

Ahh, I didn't notice your m(R), so didn't quite get what you were doing! Sorry-- I guess you had already done everything I said in my previous post! Ahh well, you've got it now!
 

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