A character in one of my stories wants to steal a valuable artifact from a museum. The artifact is on top of a sensitive pressure plate, which is configured to trigger an alarm if the weight changes for more than a few seconds. This character’s plan is to replace the artifact with another item(s) of identical weight, so as to avoid triggering the alarm.

The problem is, the character does not know the exact weight of the artifact—no one does. How can he remove the artifact without triggering the alarm?

Assume that that this world is identical to ours, pre-Industrial Revolution.

Fix the plate in place.

What the best way to do this is, will depend on what the pressure plate looks like.
However the key fact to remember is that the pressure plate works by being depressed by the weight on top of it. So it is not actually necessary to put something else of exact weight on a pressure plate in order to stop it from firing an alarm. It just has to not lift up when the item is removed.

Options:

1. Super Glue: If the pressure plate's mechanism is open and available to see then try spraying adhesive to lock the pressure plate in place. This is like spraying super glue into the gears of a clock to prevent the gears from moving.




2. Make a Mold: Create a mold of the pressure plate that will lock its depression in place. This one is a bit harder because any mold batter you pour on a plate will also have weight, but you could probably lift the item by the same force you are adding, since you know how much batter you are adding. The batter just needs to coil around some external object so that it can rigidly be kept in place.




3. Two tables and a metal bar: If the item is completely in the open, you can place 2 tables on either side of the plate. Adjust the height of tables until they exactly match the height of the plate. Then use 2 rigid poles (cast iron, wood) that cross over the plate and are attached to each table to lock the plates depression in place. This one adds no actual weight since the tables are supporting the poles' weight. The poles just lock the pressure plate in place by preventing it from moving up.




4. Other similar ideas. The limitations are only how fancy your thieves' gear can be, and the type of scale you are dealing with.

Those are just some basic ideas. The key concept here is to lock the pressure plate in place, rather than trying to match an unknowable weight.

I don't even know how I got to this webpage in the middle of the workday. The aversion to work is great today!

Precision Sand Swap

I'll expand on the sand idea by Cyn to explain how you would synchronize the rate of sand pouring with object lifting and put the correct amount of sand on the plate with the use of a fulcrum or pulley system.

Supplies

1. 
   Fulcrum or possibly a pulley system


2. 
   Counterweight greater than weight of object


3. Sand collecting bucket
   


4. 
   Bag of sand exactly equal to the weight of the counterweight minus the weight of the bucket.


5. Possibly some sand collecting hardware like a funnel or tube and some sort of apparatus like a y-shaped piece of metal to keep the bag of sand separate from the object.

Procedure

1. Set up the base of the fulcrum next to the object and platform with one end (A) over the object and the other end (B) away from the object. Attach the weight to end B. Attach the bag of sand to the end over the object (A). The counterweight is slightly heavier so you'll have to hold it level.




2. Now simultaneously attach end A to the object while placing the bucket on the platform. Here is where you may need a method to keep the sand from disturbing the object. The bucket will add weight to the platform, but the fulcrum, with the bag of sand lighter than the counterweight by exactly the weight of the bucket, will lift the object to exactly counteract the weight. This is the riskiest part of the operation as you will be directly disturbing both the plate and the object. There is no way to avoid a certain amount of weight fluctuation here. Be a ninja and hold your breath. The rest is easy!




3. Assuming that the bag of sand is over the bucket (if not use a funnel or tube), cut a hole in the bag. The sand will pour into the bucket, increasing the weight on the platform. At the same time, the total weight on end A of the fulcrum is decreasing, so the counterweight begins to pull the object off of the platform at the same rate.




4. As soon as the object is lifted off of the platform, immediately plug or move the bag to stop it from spilling more sand into the bucket.

This solution depends on the pressure plate being bigger than the object being stolen.

It does not solve the problem of weight distribution across the plate if there are multiple sensors underneath, perhaps one at each corner. In this case even though the overall weight stays the same, the distribution across sensors could change and trigger the alarm.

Note also that the counterweight and sand (plus bucket) being equal assumes that the arms of the fulcrum are equal length. You can adjust weights and arm lengths of the initial setup as long as the fulcrum stays balanced.

And... back to work.

Sand

This is hardly original, I'm sure I've seen it in various movies. Fill a small bag with sand, enough to be more than the weight of the object (have a friend holding another bag just in case it turns out to be lead). Pierce the bag and let the sand slowly pour out as you gently lift the artifact (with straps or help from another human if it's large). If the area with the pressure plate isn't very large, make the first weight transfer a properly shaped container to hold the sand and fit perfectly on the pressure plate next to the artifact.

Because you're writing the story, this difficult task will turn out perfectly right. Or right until the very end when suddenly the thief goofs, the alarm goes off, and the thief grabs the item and runs (which is what s/he should have done in the first place).

Any pre-industrial alarm system will have a bit of flexibility. Either the weight doesn't have to be exact, or the time it takes to make the alarm sound, or the time for the guards to arrive, is just barely enough for the thief to get away (or almost get away, depending on your story).

Go buy a luggage hand scale (or custom make one for greater sensitivity). Attach it to the item and as you lift it up, add extra weights to the pressure plate to balance it out. You can use anything for a weight as long as you can add it in increments. So sand and iron weights would allow you to basically get the exact weight you want.

If you have an even better setup, you could attach the scale to a solid base that doesn't move and lift the item with a motor and have it auto dispense the weight it is lifting.

Sync's Precision Sand Swap will work if you have enough space on the pressure plate to dump the sand, and if you can ensure the two sand flows are at identical mass per second. But a much simpler method is available if the "weight changes for more than a few seconds" comment in the question is valid. Either bring a spring scale or a two-pan balance in which one pan is swapped with an attachment that can be tethered to the top of the object.

With the spring balance, just lift the object fairly quickly to determine its weight, then gently drop it down again. Should be possible to do this in less than 'a few seconds'. Then Make up an identical weight (sack of sand, brass weights etc.) and quickly lift the object and place the weights. Once again the "few seconds" grace should ensure the alarm doesn't ring.

With the two-pan balance. Connect the first side of the balance to your mystery object. Place a small weight in the second side of the balance while holding it up by hand. Let go of the balance and see if the object rises off the plate. Then, de-weight the second balance. Repeat, increasing or decreasing weight two till it exactly balances. Then, once again, the "few seconds" will give you time to swap the two weights.