Measuring the upthrust
We now know that upthrust exists. The next question is what fixes its size.
Activity 15.4
- Take a cubical piece of metal and mark it so that exactly half its volume is indicated.
- Hang it from a spring balance and weigh it in air.
- Take a suitable beaker and measure its weight.
- Immerse the metal to the levels shown in each of the cases (a), (b), (c) and (d), and measure the spring balance reading and the weight of the beaker with the displaced water.
Figure to be added
The readings one student obtained
| Case | Spring balance reading (N) | Weight of beaker with displaced water (N) |
|---|---|---|
| a — cube near the water surface | 1.2 | 1.3 |
| b — cube half immersed | 0.9 | 1.6 |
| c — fully immersed, near the surface | 0.6 | 1.9 |
| d — fully immersed, lower in the water | 0.6 | 1.9 |
What the readings work out to
upthrust = weight in air − spring balance reading. Weight of displaced water = weight of the beaker − weight of the empty beaker.
| Case | Upthrust (N) | Weight of water displaced (N) |
|---|---|---|
| a | 0 | 0 |
| b | 0.3 | 0.3 |
| c | 0.6 | 0.6 |
| d | 0.6 | 0.6 |
The two columns are the same
In every case the upthrust is exactly equal to the weight of the water displaced by the object.
Note too that the readings for c and d are identical — once the object is fully immersed, taking it deeper does not change the volume of water displaced, so the upthrust does not change either.