Simple Quiz… Missing Weight

[Neil WyattModerator @neilwyatt]

[Neil WyattModerator @neilwyatt]

I have a kitchen scale, an old style pan balance.

But I only have the 2lb weight!

I have loads of scrap to make weights from, but no access to another weighing device.

What's the quickest way to make a set of weights that will weigh anything from 1 ounce to 4lbs?

 

Neil

Edited By Neil Wyatt on 01/07/2022 11:27:55

[JasonBModerator @jasonb]

Isn't it about time you went metric

The 4lbs one is easy, weigh two lots of scrap so they measure 2lbs each and then combine the two.

[David NobleParticipant @davidnoble71990]

Weigh 2lbs of scrap then divide it so that the two halves balance that will give you two 1lb weights. Then just do the same with the 1lb weight to give you 8oz then 4oz etc.

Much more difficult in metric!

 

David

Edited By David Noble on 01/07/2022 11:40:16

[HopperParticipant @hopper]

Get a bunch of coins of the same denomination and see how many it takes to equal your two pound weight then divide the number of coins into 2LB and use that to calculate ounce weights?

[JasonBModerator @jasonb]

You don't say what form the scrap is in or if you are able to use other tools. If it is lengths of bar and you have tools then keep cutting bits off a bar until it weighs 2lbs. Then measure that length of bar and simply cut others a proportional length to get the required weights.

[duncan webster 1Participant @duncanwebster1]

Density of mild steel is 0.283 lbm/cu.in. All you need now is a calculator.

[Anonymous]

The problem is incompletely specified, what about weighing 1.5 ounces?

Andrew

[roy entwistleParticipant @royentwistle24699]

Andrew He hasn't asked about 1/1/2 oz. but all he's got to do is halve the 1oz

Roy

[Anonymous]

Roy, I'm afraid you missed my point. The implication is that the set of new weights needs to be able to weigh from 1 ounce to 4 pounds in 1 ounce steps. But that is not explicitly stated. Instead it says anything from 1 ounce to 4 lbs, in which case 1.5 ounces is valid, as would be 1.25 ounces or 1.75 ounces, in fact an infinite number of weights.

Andrew

[Nick Clarke 3Participant @nickclarke3]

This is an engineer's problem. The customer services's answer would be that you are trying to weigh things weighing the wrong amount.

[JasonBModerator @jasonb]

It's obviously a problem that has been weighing on Neil's mind for some time. Probably better to weigh in the scrap and buy a set of digital scales with the money then all increments will be covered.

[SillyOldDufferModerator @sillyoldduffer]

Making my head hurt, if I've read the exam question correctly.

My bold: What's the quickest way to make a set of weights that will weigh anything from 1 ounce to 4lbs?

I think another way of wording the question is: 'what's the smallest number of individual weights that can balance any weight between 1oz and 4lbs in 1oz increments?' If it helps, and I'm not sure it does, it might be possible to reduce the total number weights to be made by adding one or more of them to the unknown side, as in 3oz unknown + 1 oz standard balances a 4 oz standard, potentially eliminating the need for a 2oz.

I don't think this is as simple as just dividing or multiplying by two because that way means a lot of individual weights are needed to measure anything between one ounce and 4 pounds in one ounce increments. For example solving the problem by making 64 one ounce weights breaks the quickest way rule. The process is easy but a lot of them have to be made, which takes time.

The way I read it, metric versus Imperial is a red-herring!

Dave

[JasonBModerator @jasonb]

You don't need lots of weights Dave, they were never supplied with 64 1oz weights. You just juggle the combinations eg 5oz would not need 5 individual 1oz weights just a 1oz and a 4oz

Edited By JasonB on 01/07/2022 13:07:32

[SillyOldDufferModerator @sillyoldduffer]

Posted by JasonB on 01/07/2022 13:07:09:

You don't need lots of weights Dave, they were never supplied with 64 1oz weights. You just juggle the combinations eg 5oz would not need 5 individual 1oz weights just a 1oz and a 4oz

…

My daft example was meant to demonstrate why at least one simple answer is off course, not as a serious suggestion!

Agreed you have to juggle combinations, but what's the minimum number of weights needed to balance an unknown in the range 1 to 64 ounces in 1 oz steps, and what are their values?

In a variant of the question found on the web, any value between 1 and 40 can be balanced with just 4 weights: 1, 3, 9, and 27.

Dave

[Nick Clarke 3Participant @nickclarke3]

While one always applauds recycling – looking at a set of 8-4-2-1-1/2oz brass weights on the 'bay I think I would save the scrap for the next project.

[JasonBModerator @jasonb]

1, 2, 4, 8, 16 (1Ibs) and 32 twice (2 x 2lbs) to get from 1-64 inclusive. You could also do it with 32 and 64oz weights rather than 2 x 32 but that would use up more of Neil's scrap

How would you weigh say 20 with a combination of 1, 3, 9 and 27?

 

Edited By JasonB on 01/07/2022 13:43:16

[V8EngParticipant @v8eng]

I would try the lazy way first and trawl the local charity shops or eBay but that’s just me!

[Thor 🇳🇴Participant @thor]

Several good answers, Neil, if you have access to something to measure volume of liquid, you could use a certain volume of water to get the weights you need (you would of course, have to tare the container). Handy calculator here.

Thor
 

Edited By Thor 🇳🇴 on 01/07/2022 13:51:39

[Mike PooleParticipant @mikepoole82104]

Posted by JasonB on 01/07/2022 13:38:57:

1, 2, 4, 8, 16 (1Ibs) and 32 twice (2 x 2lbs) to get from 1-64 inclusive. You could also do it with 32 and 64oz weights rather than 2 x 32 but that would use up more of Neil's scrap

How would you weigh say 20 with a combination of 1, 3, 9 and 27?

Edited By JasonB on 01/07/2022 13:43:16

I would put the 27 and 3 on one side and the 9 and 1 on the other, add the item to be weighed until balanced.

Mike

[Paul LousickParticipant @paullousick59116]

If you don't have a weigh scale, bathroom scale, etc, you could use a a liquid measure of water.

The imperial fluid ounce is the volume of 1 avoirdupois ounce of water at 62° F., so you could use a liquid measure of water to determine the size of the steel "weight" with a simple balance.

[Roderick JenkinsParticipant @roderickjenkins93242]

1,2,2,5 and then units of 10, 20, 20 and 50. Decades ago I authored an article in ME on making a balance and suggested using silver steel since the composition and thus density is better controlled than mild steel, as is the diameter so that only the length needs to be accurately cut to give a specific weight. I measured several batches of silver steel to give a density of 4.50 oz/cu"

Rod

[SillyOldDufferModerator @sillyoldduffer]

Posted by Mike Poole on 01/07/2022 13:53:54:

Posted by JasonB on 01/07/2022 13:38:57:

1, 2, 4, 8, 16 (1Ibs) and 32 twice (2 x 2lbs) to get from 1-64 inclusive. You could also do it with 32 and 64oz weights rather than 2 x 32 but that would use up more of Neil's scrap

How would you weigh say 20 with a combination of 1, 3, 9 and 27?

Edited By JasonB on 01/07/2022 13:43:16

I would put the 27 and 3 on one side and the 9 and 1 on the other, add the item to be weighed until balanced.

Mike

Just so.

I've not checked, but noting 1, 3, 9 and 27 are rising powers of 3, I predict the 5th weight needed to answer Neil's question is 81 ounces.

Actually this set of 5 weight goes well beyond 4lbs – up to 7lbs 9oz if I'm right. (I hope no-one has forgotten my maths is terrible.)

Not too difficult getting a 1oz weight from 2lb with a balance, but building the rest of the set in powers of 3 will be fun! Another disadvantage of the 5 weight system is the arithmetic needed to work in pounds and ounces from a base 3 set of weights. No problem though – imperial weights and measures were riddled with strange conversions, and no-one complained about the sums, allegedly.

Dave

[Martin ConnellyParticipant @martinconnelly55370]

The simplest solution would be to go back to the historically commonplace offset beam balance. It was the weighing system used for thousands of years that used the minimum of materials and parts, was robust and was easy to carry if you were travelling.

Martin C

[Howard LewisParticipant @howardlewis46836]

It would seem likely that, the balance being old is Imperial, so the weights would increment a a geometric progression with a factor of 2.

So one of each of: 1/2 oz, 1, 2, 4, 8, 16 would allow items weighing up to 31 1/2 ounces to be measured in 1/2 oz increments. . Duplicating some or all of the weights would extend the range.

Methods of determining the missing weights have already been described, so as long as one weight is available, the others ought to be to be derived by using temporary ones to halve or double them datum weight.

For greater precision the way is to drill and tap a hole and fit a grubscrew. The weight can then be adjusted to the desired level more accurately by adding lead shot under the grubscrew.

This was the method advocated by the local Weights and Measures Inspector when we needed a set of standard weights for calibrating dynamometers. He was apologetic that the 25 and 50 lb weights would not be closer than a few grains!

Howard.

[Author]

Posts