The mass of a penny is 2.5g. If a boat can hold 22 pennies before sinking, what is the mass of the water it displaces? (The density of water is 1.0 g/cm3)

Question

anonymous · Answer

Something sinks when it displaces less mass of water than it has itself.

theeric · Answer

The buoyant force is always equal to the weight of the displaced fluid.

An object can float if the buoyant force is greater than or equal to the weight of the object.

A sinking object will still have such buoyant force, but its weight is greater than buoyant force.

|dw:1389497512217:dw|It's left floating when it's weight is 22 pennies, but will sink if there is any more weight.
So, with 22 pennies, the weight equals the buoyant force.

And so you know the buoyant force, which is also the weight of the water.
If you know the weight, you can find the mass.
Since you know the mass and the density, you can then find the volume.

$\rm{density=\dfrac{mass}{volume}}$

anonymous · Answer

Thanks!

theeric · Answer

You're welcome! :)