Forces_Concept_6

Subject Facts

Density and mass

'Floating and sinking' is frequently regarded as a set of ideas that can be covered through water play early on a child's formal education; but in reality, it involves using some key scientific and mathematical ideas. One of the first big steps to be made is from 'heaviness' to 'density. In the same way that children tend to confuse 'volume' with the level of liquid, they often confuse density and mass.

Mass (see Forces) is the amount of 'stuff' in an object,

Density is the amount of 'stuff' per unit of volume, In general terms, materials that are denser than water sink in water; :those that are less dense will float. The density cf water is a building block of the metric system: one kilogram (l kg) is defined as the mass of one iitre (1L) of water, One litre is 1000 cubic centimetres (1 000cm ³), and I kg is 1 000g, so the mass of I ml (or l.cm ³) of water is lg. The density of water is thus Ig per crn ³ (lg/ cm ³ or gcm-3).Thus anything with a density of less than 1 g/cm ³ will float on water, and anything with a greater density will sink

Finding out the density

Finding the density of a ægutar object (such as a cube) is relatively easy. You just measure the external dimensions, calculate the volume, measure the mass (by weighing the object) and divide the mass by the volume, Irregular objects are more of a challenge. Finding the mass poses no additional but how do you determine the voiume?

If you submerge an object in water; it will displace exactly its own volume of water. if you fill a bath to the very top, then get and submerge yourself entirely, you will find yourself moppng exactly your own volume of water from the bathroom floor. If you were to use a bucket with a pouring spout on the side, fill it with water up to the spout and then submerge an object (such as a brick) in the water, the object will displace its own volume in water through the spout. This excess water can be collected in a measuring jug. Now you know the volume, you can calculate the :density,

A simple way to compare the densities of an object and water would be to place the object on one side of a balance and the water it has displaced on the other side. If the object goes down, it would sink if it goes up, would float.

'Eureka!'

Archimedes' famous cry (meaning have found it!) was his reaction to solving a scientific problem. The king had a gold crown that he suspected was fake. He thought that the goldsmith had stolen some of the gold and added lead, a heavier metal, to make up the correct weight. How could he prove it? Archimedes' solution came to him in the bath, It was to take some lumps of pure gold and balance them against the suspect crown, then immerse both in water to see how much water was displaced. The lumps of gold had a greater volume than the crown, proving that the crown was not pure gold: some of it was a denser metal (lead).

Upthrust

For an object to float on water; the upward push of the water must equal the downward pull of gravity on the object (as with the book and the table). You can see the effect of the upward push, or upthrust when an object floats, if you push down on a swimming float a pool, or a rubber duck in the bath, you can feel the upthrust of the water. You can also feel how much downward force you have to in addition to the pull of gravity, to balance this upthrust. But does this upthrust just 'switch off' when an object sinks?

Think about what happens when you are standing in a swimmng pool, up to your neck in water. You can bounce around and almost float in an upright position, as if you were nearly weightless. When you climb out onto the side of the pool, gravity seems to take over once more: it is much harder to lift yourself. So when you are in the water; up-thrust or buoyancy has an effect on you whether you are floating or not.

Now consider an object that sinks rapidly. You may have a set of blocks of materials at school .Take a metal block or something similar and tie some string around it (see Figure 1) so that you can attach a long, thin rubber band. Lift the block by the rubber band and note how much the band stretches. Take the block overto a bucket of water and slowly lower it in. The band contracts as the block is lowered into the water and reaches minimum when the block is fully submerged. Note how long the band is now. Take the block out; the band will stretch once more. Put your hand under the block and support it until the band contracts to the length that it had when the block was in the water. You can now feel the force that the water was pushing the block up with: not enough to make it float, but a very noticeable upthrust.

With any object that sinks (that is, is made from a material denser than water) the upthrust will be equal to the weight of a volume of water equal to the volume of the object. So if you held up the block to imitate the upthrust of water in one hand and held the overflow from the bucket (an amount of water with the same volume as the block) in the other; the force on both hands would feel the same.

That sinking feeling

You may have noticed that things fall through the air much more quickly than they fall through water. This is partly because water is 'thicker' than air and so it resists movement through it (by friction) more effectivey. It is also because the upthrust of water is much greater than that of air: the water pushes up on the object, and may even keep it afloat, For a sinking object. the force of gravity is effectively reduced by the upthrust acting on it..