Whether an object floats or sinks or does neither will depend on its weight or the force that pushes the object down and its buoyant force or the force that pushes the object up.
First, let us consider the case where the object neither float nor sink.
Common sense tells us that when the object neither sinks nor floats, the force that pushes the object up (buoyant force) is equal to the force that pushes the object down (weight)
This fact will help us deduct something important about the density of the object and the density of water.
Let us suppose that
Buoyant force = weight of object (1)
We also saw the following in the lesson about Archimedes' principle
Buoyant force = weight of displaced water (2)
Putting equations (1) and (2) together will give us
weight of object = buoyant force = weight of displaced water
We can then make this conclusion
We need two more things in order to make our conclusion.
First, we saw in the lesson about buoyant force that the volume of the object is equal to the volume of the displaced water.
Second, we need the formula for density.
Let us put it all together!
Weight of object = weight of displaced water
volume of object = volume of displaced water
What does this tell us about the density?
Suppose weight of object = weight of displaced water = 5 NSuppose volume of object = volume of displaced water = 5 cm3
Suppose buoyant force > weight of object, the object will float.
Weight of object < buoyant force
Since buoyant force = weight of displaced water,
we get weight of object < weight of displaced water
And again, we know volume of object = volume of displaced water
Suppose weight of object = 4 N and weight of displaced water = 5 NSuppose volume of object = volume of displaced water = 5 cm3
Why do things float then?
Here is the summary to determine when an object will float, sink, or do neither.