2. A rectangular barge 7 m long and 2 m wide floats in fresh water. How much will the barge sink when loaded with 600 kg of sand? Show all calculations leading to an answer.

What makes any object float?

The object displaces an amount of water that has

the same weight as the floating object.

The heavier the object is, the more water it has to displace

in order to float.

The barge is originally floating, so we know that it must be displacing

its own weight in water.

Then somebody comes along and dumps another 600 kg onto it.

Now suddenly, the barge is heavier. So in order to keep floating,

it has to displace some more water.

However much the extra 600 kg weighs, it has to displace 600 kg

of water.

We're really happy that the whole thing is happening in water, because

that makes the calculation easy ... 1 kg is the mass of 1 liter of water!

With the added load, the barge has to displace 600 more liters of water.

Well, there are 1,000 liters in 1 cubic meter ... 600 liters = 0.600 meter³.

The barge has to settle a little lower in the water, just enough to displace

another 0.6 m³ of water.

As the barge groans and settles deeper in the water, how much new

volume of water does it displace?

Extra Volume = (length) x (width) x (extra distance it sinks).

It needs to displace 0.6 m³ of extra volume.

0.6 m³ = (7 m) x (2 m) x (extra distance it sinks)

Divide each side

by (7m) x (2m) : 0.6 m³ / (7m x 2m) = extra distance it sinks

Additional depth = 0.6 m³ / 14 m²

= 0.0429 meter

= 43 millimeters (rounded)

Is that cool or what?!