Remember that arrows are proportionally longer as the vectors they represent increase in magnitude.
STS
Have you ever noticed that when ice melts in your drink, the level of the drink does not rise? This is because the ice was already partially immersed and so had already displaced the fluid before melting (Fig. 5.12).
Archimedes’ principle
Since pressure acts in all directions, then it must act on the base of an object, pushing up, as well as on the top, pushing down (Fig. 5.11).
Archimedes’ principle
Whenever an object is totally or partially immersed in a fluid, it experiences an upthrust that is equal to the weight of the fluid it displaces.
FIG. 5.11 Pressure acts in all direction but is stronger at the object’s base because of increased depth
Notice that the force arrows on the base of the object in Fig. 5.11 are bigger than those on the top. The larger forces on the object’s base are due to increased depth.
This upward force is named upthrust or buoyancy. Its size is given by Archimedes’ principle.
FIG. 5.12 Ice in a drink displaces the liquid
Archimedes’ principle explains how ships float and why icebergs have already displaced the water they are floating in.
u To demonstrate Archimedes’ principle
1. Find the weight of an empty beaker. 2. Fill an overflow can to the top and let it settle. 3. Place the empty beaker under the spout of the overflow can.
4. Place a stone in the overflow can, by lowering it from a newton balance. You can record the weight of the stone from the balance at this point.
5. The water will flow from the overflow can into the beaker (Fig. 5.13b).
6. Find the weight of the beaker now. 7. Subtract the weight of the empty beaker from the weight of the beaker and water. This weight should equal the difference between the weight of the stone in the water and its weight in the air (upthrust).
8. To verify, compare the weight from the newton balance to that found from the beaker. 9. Upthrust = weight of fluid displaced
