It’s one of the shortcomings of having tests that supply the answers but not the methodology. We need your help. We know the question. We know the answer. We can’t connect them. Can you help us?

A rectangular barge 5.0m long and 2.0m wide, floats in fresh water. How much deeper will it float when its load is a 500kg horse?

Answer: 5cm

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Ooh I think you need Archimedes Principle for this one…

http://en.wikipedia.org/wiki/Archimedes%27_principle

Ooh also, this bit is longwinded but is very useful – includes the formula you need to work out the density that the horse adds to the barge, and mentions other experiments you can do to help learn the principle…

http://hyperphysics.phy-astr.gsu.edu/hbase/class/phscilab/dens.html

1 gram of water takes up 1 cubic cm.

500 kg horse = 500,000 g horse, so it should displace 500,000 cu cm water. The barge’s area is 500 cm x 200 cm = 100,000 square cm. 5 cm (depth) x 100,000 (area) = volume water displaced.

Yes, basically you’re displacing 500 additional kg (i.e. 500 additional litres) of water. You just have to spread that 500 litres over the L&W dimensions of the barge. 500 litres is 500,000 cm^3, so divide that volume by the L & W of the barge to get the depth to which it sinks in order to displace the additional amount.

The explanations above are correct, but sometimes multiple slightly different explanations help.

is this some archemidis principle if i am not mistaken?