1. A101 Science Problem 03: Hang, Float and Sink 6th Presentation

2. Understanding the problem
Set-up 1
Set-up 2 ?
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.
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?

3. Observations
Smaller reading
Larger reading ? ?
Set-up 1
Set-up 2 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.
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.

4. 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.
Please note that the above are only true when the other factors, such as size of container and thickness of string, are identical for both setups.
The deduction is still valid, even if we change the mass and/or the shape of the hanging object.

5. 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.

6. Accounting for the weighing scale readings
Volume of submerged portion of object = 10 cm x 10 cm x 2 cm = 200 cm3
Equivalent volume of water = 200 cm3
Mass of equivalent volume of water = Volume x density = 200 cm3 x 1 g/cm = 200 g
Volume
= 200 cm3
Additional water of 200 cm3
Same weighing scale readings!

7. Apparent mass of water added: 2000 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
Reading on the weighing scale (g)
Deflected path due to the presence of object
Apparent mass of water added: 2000 g
2000 ? ?
Actual Contribution from water to weighing scale reading = 1500 g
1000
Water fully immerses the object
1500 g of water added
Hanging
No Object
Initial
Reading
400 g
1000
2000
3000
Mass of water
added (g)
Water level touching the bottom surface of the object

8. 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.

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

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

11. 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 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.

12. 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.

13. 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.
more than
less than
equal to