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This is another old O level applied mathematics problem regarding moments. It reads as follows:

A rod $PQ$ is $5 ft.$ long. When a $1 lb.$ mass is hung from $P$ and a $3 lb.$ mas is hung from $Q$, the rod balances at a point $42 in.$ from $P$. When the masses are interchanged, the rod balances at a point $22 in.$ from $P$. Calculate the mass of the rod and the distance of its centre of gravity from $P$.

Solution gives:

$mass = 21 lb.$
$dist. from$ $P = 3 ft.$

I am able to get the distance of $3 ft.$ but am getting the mass of the rod to be $2 lb.$ This seems to be a little light but as I can not obtain the answer for mass given as solution, I am wondering if there is a typo in the book.

If anyone can offer any assistance I would be very grateful.

Not very good at computer code so hope this attachment helps.

part 1

part 2

Many thanks for any help or advice once again.

GR L
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  • It would help if you showed us your calculations. – saulspatz Jul 22 '21 at 21:42
  • Yes please do. There is a lot of arithmetic/algebra here and we should not have to reinvent any more wheels than necessary. – Oscar Lanzi Jul 22 '21 at 22:56
  • Sounds like this will not work. – Oscar Lanzi Jul 23 '21 at 09:29
  • @OscarLanzi Apologies. I am not sure if there is another way to show you calculations other than leaving a comment but here goes. Let x represent distance of centre of gravity from Q, W the weight of the rod and R the reaction in the two instances given. Taking moments about Q gave the following two equations: Wx + 15 = 3R/2 (1) Wx + 35 = 19R/6 (2) also up forces = down forces so R = 4 + W (3) (3) into (1) and (2) respectively gives: (2x - 3)W = 2 (4) (19 - 6x)W = 14 (5) rearranging and equating (4) and (5) gives my result where x is distance from Q. – GR L Jul 23 '21 at 09:30
  • @OscarLanzi Hello again. I have added an attachment to show my working. If you can see a mistake in my reasoning then I would be extremely grateful if you could let me know. I've been at this for some time now but can not see an error. Many thanks. – GR L Jul 23 '21 at 19:18
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    It is out of focus! – Cesareo Jul 23 '21 at 19:21
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    I'm afraid your picture is illegible. – TonyK Jul 23 '21 at 19:21
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    I'm sorry. I will try and take the picture again. – GR L Jul 23 '21 at 19:23
  • Ironically, your very own picture ends with the conclusion $W=21$. Just look at it! (Please don't edit it out -- it is a perfect mistake.) – TonyK Jul 23 '21 at 21:20
  • @TonyK It’s actually the l from pound abbreviation ie lb, I just missed a little off when taking the picture - not too good with technology I’m afraid. However, I agree it does look like I’ve given the answer of 21 so I will leave alone and not edit. Many thanks once again. – GR L Jul 24 '21 at 08:22

1 Answers1

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Yes, it's a misprint. I did the calculations (independently of your illegible working!), and I got a mass of 2 lb.

TonyK
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  • Thank you very much, I have tried to upload new pictures if they help at all. Once again, many thanks for taking the time to reply. – GR L Jul 23 '21 at 19:44