Weigh something with multiple scales

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Weighing a 40inX48in wooden pallet using four bathroom scales is feasible if the weight is evenly distributed. Each scale can measure up to 300lbs, so the total weight of the pallet and boxes should not exceed this limit per scale. To obtain the total weight, the readings from all four scales should be summed together. Proper positioning and simultaneous lowering of the pallet onto the scales are crucial for accurate measurements. Conducting this experiment can provide practical insights into the principles of physics.
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First off I'm not in school and therefore my question isn't for homework. This is more of a question as to whether something is possible based on physics. However, I think the course-work section is the best spot for this.

Homework Statement



Is it possible to weigh a standard wooden pallet 40inX48in using 4 bathroom scales at the 4 corners?

Givens:
Max weight of pallet with boxes: 750lbs
Max measurable weight of bathroom scales: 300lbs

Assumptions:
Weight of boxes on pallet is evenly distributed
Weight of pallet with boxes is evenly distributed across the 4 scales

1. Is this even possible or will the scales simply be crushed?
2. If it is possible, and I gather 4 weights, from the 4 scales, at 4 corners, do I add the weights together or average them? Or is the calculation more complicated than this?


Homework Equations




The Attempt at a Solution



Regards
-nutso
 
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Hey, borrow your neighbour's scales, get into your bathroom and stand one foot on each pair of scales. Physics is about experiments!
 
The total force downwards (the weight of the pallet), must be reacted by a total and equal opposite reaction force (from the scales).

if you spread the weight exactly evenly over the four scales, you would measure the total mass of the pallet over all the scales. In other words, you would have to add the masses that you read on the scales to get the total mass.

you'll have to:
position the scales very well on a flat surface
lower the pallet onto all four evenly and at the same time
make sure the gauge part is sticking out so that you can read the measurements :wink:

Take some photos and let us know how it goes.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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