A 101 Science Problem 03 Hang Float and

Understanding the problem • Before water touched the bottom of the hanging object, the weighing scale reading for both setups were the same when the same amount of water was added. ? ? Set-up 1 Set-up 2 • The reading was equal to the sum of the mass of the container and the mass of water added. • If we continue adding water, will the weighing scale readings for the two setups still remain equal?

Observations Smaller reading Larger reading h ? Set-up 1 ? Set-up 2 Even though we added the same amount of water to each container, the weighing scale reading for the container with the partially submerged object was greater. h ? ? Set-up 1 Set-up 2 However, when the water levels in both containers were the same, experiment showed that the weighing scale readings were the same even though there was more water in set-up 1.

Deduction • Based on the experiment, we can make a preliminary deduction that with the same height of the water level, the weighing scale reading would be the same, regardless of the amount of water added or the presence of any partially submerged object. • The deduction is still valid, even if we change the mass and/or the shape of the hanging object.

A possible explanation • A container has no way of knowing what is immersed in the water; it can only feel a downward ‘push’ from the water which is dependent on the height of the water level. • Once the height of the water levels are the same in both cases, both containers will experience the same amount of 'push' from the water, so both weighing scales will end up showing the same reading. • It is possible to have other valid explanations for the deduction.

Accounting for the weighing scale readings • Volume of submerged portion of object = 10 cm x 2 cm = 200 cm 3 • Equivalent volume of water = 200 cm 3 • Mass of equivalent volume of water = Volume x density = 200 cm 3 x 1 g/cm 3 = 200 g Additional water of 200 cm 3 Volume = 200 cm 3 Same weighing scale readings!

Reading on the weighing scale (g) Graph of reading (g) vs water added (g) Once the object is fully immersed, the weight of added water gets duly reflected on the weighing scale. ? 3000 Contribution from hanging object: Volume occupied by object equivalent to 500 g of water Deflected path due to the presence of object 2000 ? Actual Contribution from water to weighing scale reading = 1500 g ? 1000 1500 g of water added Initial Reading 400 g 0 Apparent mass of water added: 2000 g 1000 Water level touching the bottom surface of the object 2000 Water fully immerses the object 3000 Hanging No Object Mass of water added (g)

Case of floating • In some cases, the equivalent mass of water due to the volume submerged by some partially submerged objects is equal to the mass of the object itself. • When this happens, the object floats. • Hence, for floating objects like wood, there is a maximum volume which is submerged in water. • This usually occurs when the density of the object is lower than that of water.

Case of floating No tension Cord slackens; in the object cord floats now Object Maximum volume object can be immersed in water

Reading on the weighing scale (g) Graph of reading(g) vs water added(g) ? 3000 Response if the object does not float Object begins to float. 2000 ? The maximum addition in weight the object can make is 200 g ? 1000 Initial Reading 400 g 0 Object floats when more water is added. 600 g of water added 1000 Water level touching the bottom surface of the object Hanging Floating No Object 2000 3000 Mass of water added (g)

Going further • When the string holding the suspended object is cut and the object sinks to the base of the container, the reading on the weighing scale is equal to the sum of mass of the object, the water added and the container, because the full mass of the object acts on the weighing scale. • For example, when a 500 g object is hung by a string and fully submerged in a 400 g container containing 400 g of water, the weighing scale reading is 1100 g. When the string is cut and the object sinks to the base of the container, the weighing scale reading is 1300 g.

Learning Points • Based on our experiment in the video, the immersion of the object into the water causes an increase in the weighing scale reading. • Comparing two setups, one with and the other without a hanging object, we found that as long as the height of the water levels are equal the weighing scale readings will be equal. • The volume of the submerged portion of the object causes an increase in weighing scale reading. This increase is equal to the mass of the same volume of the liquid. • To explain the phenomenon observed in the video, we made use of various skills such as making observations and deductions, testing and verifying results and drawing conclusions.

Discussion Two cylindrical containers with different radius are being filled with water as shown below. The reading on Weighing Scale C is ______ the reading on Weighing Scale D. a. more than b. less than c. equal to